SOLUTION: I NEED SOME HELP WITH SOME PROBLEMS ON QUADRATIC EQUATIONS.... 1) (2+X)SQUARED=49 2) (X+2)(3X-4)=(X+5)(2X-5) 3)CAN NOT TELL IF THE EQUATION IS RATIONAL OR IRRATIONAL...8XSQUA

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Question 105663This question is from textbook college algebra
: I NEED SOME HELP WITH SOME PROBLEMS ON QUADRATIC EQUATIONS....
1) (2+X)SQUARED=49
2) (X+2)(3X-4)=(X+5)(2X-5)
3)CAN NOT TELL IF THE EQUATION IS RATIONAL OR IRRATIONAL...8XSQUARED=14X-3
4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0
 This question is from textbook college algebra

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1) (2+X)SQUARED=49
%282%2Bx%29%5E2+=+49 find square root on both sides
sqrt%28%282%2Bx%29%5E2%29+=+sqrt%2849%29

2%2Bx+=+7
x+=+7-2
x+=+5

2) %28X%2B2%29%283X-4%29=%28X%2B5%29%282X-5%29 multiply terms on both sides
3x%5E2+-+4x+%2B+6x+-+8+=+2x%5E2+-+5x+%2B+10x+-+25 add like terms on both sides

3x%5E2+%2B+2x-+8+=+2x%5E2+%2B+5x+-+25 add -2x%5E2 to both sides

3x%5E2+-+2x%5E2+%2B+2x-+8+=+2x%5E2+-+2x%5E2+%2B+5x+-+25
x%5E2+%2B+2x+-+8+=+5x+-+25 add -5x to both sides
x%5E2+%2B+2x+-+5x++-+8+=+5x+-+5x++-+25
x%5E2+-+3x-+8+=+-+25 add %2B+25 to both sides
x%5E2+-+3x+-+8+%2B+25+=+-+25+%2B25
x%5E2+-+3x+%2B+17+=+0

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-3%2Ax%2B17=0 ( notice a=1, b=-3, and c=17)





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




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29 Negate -3 to get 3




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.)




x+=+%283+%2B-+sqrt%28+9%2B-68+%29%29%2F%282%2A1%29 Multiply -4%2A17%2A1 to get -68




x+=+%283+%2B-+sqrt%28+-59+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




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)




x+=+%283+%2B-+i%2Asqrt%2859%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


x=3%2F2%2Bsqrt%2859%29%2F2%2Ai or x=3%2F2-sqrt%2859%29%2F2%2Ai









3)EQUATION IS RATIONAL....8XSQUARED=14X-3
8x%5E2+=+14x+-+3
8x%5E2+-+14x+%2B3+=+0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 8%2Ax%5E2-14%2Ax%2B3=0 ( notice a=8, b=-14, and c=3)





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




x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%2A8%2A3+%29%29%2F%282%2A8%29 Negate -14 to get 14




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.)




x+=+%2814+%2B-+sqrt%28+196%2B-96+%29%29%2F%282%2A8%29 Multiply -4%2A3%2A8 to get -96




x+=+%2814+%2B-+sqrt%28+100+%29%29%2F%282%2A8%29 Combine like terms in the radicand (everything under the square root)




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)




x+=+%2814+%2B-+10%29%2F16 Multiply 2 and 8 to get 16


So now the expression breaks down into two parts


x+=+%2814+%2B+10%29%2F16 or x+=+%2814+-+10%29%2F16


Lets look at the first part:


x=%2814+%2B+10%29%2F16


x=24%2F16 Add the terms in the numerator

x=3%2F2 Divide


So one answer is

x=3%2F2




Now lets look at the second part:


x=%2814+-+10%29%2F16


x=4%2F16 Subtract the terms in the numerator

x=1%2F4 Divide


So another answer is

x=1%2F4


So our solutions are:

x=3%2F2 or x=1%2F4



4)S=SO+GTSQUARED+K FOR T WITH THE DENOMINATOR OF 0