SOLUTION: Solve by using the quadratic formula. x^2 = 5x + 8

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Question 88259: Solve by using the quadratic formula. x^2 = 5x + 8

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+5x+%2B+8+

x%5E2+-+5x+-+8=0+ Get everything to one side

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%5E2-5%2Ax-8=0 (notice a=1, b=-5, and c=-8)

x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=-5, and c=-8



x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Negate -5 to get 5



x+=+%285+%2B-+sqrt%28+25-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square -5 to get 25



x+=+%285+%2B-+sqrt%28+25%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32



x+=+%285+%2B-+sqrt%28+57+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%285+%2B-+sqrt%2857%29%29%2F%282%2A1%29 Simplify the square root



x+=+%285+%2B-+sqrt%2857%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%285+%2B+sqrt%2857%29%29%2F2 or x+=+%285+-+sqrt%2857%29%29%2F2


Which approximate to

x=6.27491721763537 or x=-1.27491721763537


So our solutions are:
x=6.27491721763537 or x=-1.27491721763537

Notice when we graph x%5E2-5%2Ax-8 we get:



when we use the root finder feature on a calculator, we find that x=6.27491721763537 and x=-1.27491721763537.So this verifies our answer.