document.write( "Question 103616: Solve equations for x\r
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\n" ); document.write( "\n" ); document.write( "(x-3)^2=10\r
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Algebra.Com's Answer #75339 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
1.
\n" ); document.write( "\"%28x-3%29%5E2=10\"
\n" ); document.write( "\"x%5E2+-6x+%2B9+=+10\"
\n" ); document.write( "\"x%5E2+-6x+%2B9+-+10+=+0\"
\n" ); document.write( "\"x%5E2+-+6x+-1+=+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%5E2-6%2Ax-1=0\" ( notice \"a=1\", \"b=-6\", and \"c=-1\")
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\n" ); document.write( " \"x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29\" Plug in a=1, b=-6, and c=-1
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\n" ); document.write( " \"x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29\" Negate -6 to get 6
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\n" ); document.write( " \"x+=+%286+%2B-+sqrt%28+36-4%2A1%2A-1+%29%29%2F%282%2A1%29\" Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because \"%28-6%29%5E2=-6%2A-6=36\".)
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\n" ); document.write( " \"x+=+%286+%2B-+sqrt%28+36%2B4+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-1%2A1\" to get \"4\"
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\n" ); document.write( " \"x+=+%286+%2B-+sqrt%28+40+%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+=+%286+%2B-+2%2Asqrt%2810%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+=+%286+%2B-+2%2Asqrt%2810%29%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%286+%2B+2%2Asqrt%2810%29%29%2F2\" or \"x+=+%286+-+2%2Asqrt%2810%29%29%2F2\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=%2B6%2F2%2B2%2Asqrt%2810%29%2F2\" or \"x=%2B6%2F2-2%2Asqrt%2810%29%2F2\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=3%2Bsqrt%2810%29\" or \"x=3-sqrt%2810%29\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=3%2Bsqrt%2810%29\" or \"x=3-sqrt%2810%29\"
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\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "\"%28x%2B2%29%5E2+=+16\"
\n" ); document.write( "\"x%5E2+%2B+4x+%2B+4+=+16\"
\n" ); document.write( "\"x%5E2+%2B+4x+%2B+4+-+16+=+0+\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+4x+-12+=+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%2B4%2Ax-12=0\" ( notice \"a=1\", \"b=4\", and \"c=-12\")
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\n" ); document.write( " \"x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-12+%29%29%2F%282%2A1%29\" Plug in a=1, b=4, and c=-12
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\n" ); document.write( " \"x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-12+%29%29%2F%282%2A1%29\" Square 4 to get 16
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\n" ); document.write( " \"x+=+%28-4+%2B-+sqrt%28+16%2B48+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-12%2A1\" to get \"48\"
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\n" ); document.write( " \"x+=+%28-4+%2B-+sqrt%28+64+%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+=+%28-4+%2B-+8%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+=+%28-4+%2B-+8%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-4+%2B+8%29%2F2\" or \"x+=+%28-4+-+8%29%2F2\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%28-4+%2B+8%29%2F2\"
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\n" ); document.write( " \"x=4%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=2\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=2\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%28-4+-+8%29%2F2\"
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\n" ); document.write( " \"x=-12%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-6\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-6\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=2\" or \"x=-6\"
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