SOLUTION: Solve for x x^2+4x+4=7 Thanks in advance.

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Question 87867: Solve for x
x^2+4x+4=7
Thanks in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B4x%2B4=7

x%5E2%2B4x%2B4-7=cross%287-7%29 Subtract 7 from both sides

x%5E2%2B4x-3=0 Combine like terms



Now let's use the quadratic formula to solve for x:
Starting with the general quadratic

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

the general form of 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%2B4%2Ax-3=0

x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=-3



x+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square 4 to get 16



x+=+%28-4+%2B-+sqrt%28+16%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12



x+=+%28-4+%2B-+sqrt%28+28+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F%282%2A1%29 Simplify the square root



x+=+%28-4+%2B-+2%2Asqrt%287%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-4+%2B+2%2Asqrt%287%29%29%2F2 or x+=+%28-4+-+2%2Asqrt%287%29%29%2F2


Which approximate to

x=0.645751311064591 or x=-4.64575131106459


So our solutions are:
x=0.645751311064591 or x=-4.64575131106459

Notice when we graph x%5E2%2B4%2Ax-3 we get:



when we use the root finder feature on a calculator, we find that x=0.645751311064591 and x=-4.64575131106459.So this verifies our answer