document.write( "Question 105663This question is from textbook college algebra
\n" ); document.write( ": I NEED SOME HELP WITH SOME PROBLEMS ON QUADRATIC EQUATIONS....
\n" ); document.write( " 1) (2+X)SQUARED=49
\n" ); document.write( " 2) (X+2)(3X-4)=(X+5)(2X-5)
\n" ); document.write( " 3)CAN NOT TELL IF THE EQUATION IS RATIONAL OR IRRATIONAL...8XSQUARED=14X-3
\n" ); document.write( " 4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0
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Algebra.Com's Answer #77025 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
1) (2+X)SQUARED=49\r
\n" ); document.write( "\n" ); document.write( "\"%282%2Bx%29%5E2+=+49\" find square root on both sides\r
\n" ); document.write( "\n" ); document.write( "\"sqrt%28%282%2Bx%29%5E2%29+=+sqrt%2849%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"2%2Bx+=+7\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+7-2\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+5\"\r
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\n" ); document.write( "\n" ); document.write( " 2) \"%28X%2B2%29%283X-4%29=%28X%2B5%29%282X-5%29\" multiply terms on both sides\r
\n" ); document.write( "\n" ); document.write( "\"3x%5E2+-+4x+%2B+6x+-+8+=+2x%5E2+-+5x+%2B+10x+-+25\" add like terms on both sides\r
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\n" ); document.write( "\n" ); document.write( "\"3x%5E2+%2B+2x-+8+=+2x%5E2+%2B+5x+-+25\" add \"-2x%5E2\" to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"3x%5E2+-+2x%5E2+%2B+2x-+8+=+2x%5E2+-+2x%5E2+%2B+5x+-+25\" \r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+2x+-+8+=+5x+-+25\" add \"-5x\" to both sides\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+2x+-+5x++-+8+=+5x+-+5x++-+25\" \r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+3x-+8+=+-+25\" add \"%2B+25\" to both sides\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+3x+-+8+%2B+25+=+-+25+%2B25\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+-+3x+%2B+17+=+0\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2-3%2Ax%2B17=0\" ( notice \"a=1\", \"b=-3\", and \"c=17\")
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\n" ); document.write( " \"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29\" Plug in a=1, b=-3, and c=17
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29\" Negate -3 to get 3
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9-4%2A1%2A17+%29%29%2F%282%2A1%29\" Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because \"%28-3%29%5E2=-3%2A-3=9\".)
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9%2B-68+%29%29%2F%282%2A1%29\" Multiply \"-4%2A17%2A1\" to get \"-68\"
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+-59+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%283+%2B-+i%2Asqrt%2859%29%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%283+%2B-+i%2Asqrt%2859%29%29%2F%282%29\" Multiply 2 and 1 to get 2
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\n" ); document.write( " After simplifying, the quadratic has roots of
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\n" ); document.write( " \"x=3%2F2%2Bsqrt%2859%29%2F2%2Ai\" or \"x=3%2F2-sqrt%2859%29%2F2%2Ai\"
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\n" ); document.write( " 3)EQUATION IS RATIONAL....8XSQUARED=14X-3\r
\n" ); document.write( "\n" ); document.write( "\"8x%5E2+=+14x+-+3\"\r
\n" ); document.write( "\n" ); document.write( "\"8x%5E2+-+14x+%2B3+=+0\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"8%2Ax%5E2-14%2Ax%2B3=0\" ( notice \"a=8\", \"b=-14\", and \"c=3\")
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\n" ); document.write( " \"x+=+%28--14+%2B-+sqrt%28+%28-14%29%5E2-4%2A8%2A3+%29%29%2F%282%2A8%29\" Plug in a=8, b=-14, and c=3
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\n" ); document.write( " \"x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%2A8%2A3+%29%29%2F%282%2A8%29\" Negate -14 to get 14
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\n" ); document.write( " \"x+=+%2814+%2B-+sqrt%28+196-4%2A8%2A3+%29%29%2F%282%2A8%29\" Square -14 to get 196 (note: remember when you square -14, you must square the negative as well. This is because \"%28-14%29%5E2=-14%2A-14=196\".)
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\n" ); document.write( " \"x+=+%2814+%2B-+sqrt%28+196%2B-96+%29%29%2F%282%2A8%29\" Multiply \"-4%2A3%2A8\" to get \"-96\"
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\n" ); document.write( " \"x+=+%2814+%2B-+sqrt%28+100+%29%29%2F%282%2A8%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%2814+%2B-+10%29%2F%282%2A8%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%2814+%2B-+10%29%2F16\" Multiply 2 and 8 to get 16
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%2814+%2B+10%29%2F16\" or \"x+=+%2814+-+10%29%2F16\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%2814+%2B+10%29%2F16\"
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\n" ); document.write( " \"x=24%2F16\" Add the terms in the numerator
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\n" ); document.write( " \"x=3%2F2\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=3%2F2\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%2814+-+10%29%2F16\"
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\n" ); document.write( " \"x=4%2F16\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=1%2F4\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=1%2F4\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=3%2F2\" or \"x=1%2F4\"
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\n" ); document.write( "\n" ); document.write( " 4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0\r
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