SOLUTION: Find the value(s)of x for which f(x)=g(x) f(x)=x^2+16x+19 g(x)= 8x+7

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Question 351791: Find the value(s)of x for which f(x)=g(x)
f(x)=x^2+16x+19 g(x)= 8x+7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=g%28x%29 Start with the given equation.


x%5E2%2B16x%2B19=8x%2B7 Plug in f%28x%29=x%5E2%2B16x%2B19 and g%28x%29=+8x%2B7


x%5E2%2B16x%2B19-8x-7=0 Get all terms to the left side.


x%5E2%2B8x%2B12=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=8, and c=12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%2812%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=12


x+=+%28-8+%2B-+sqrt%28+64-4%281%29%2812%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-48+%29%29%2F%282%281%29%29 Multiply 4%281%29%2812%29 to get 48


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Subtract 48 from 64 to get 16


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-8+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


x+=+%28-8+%2B+4%29%2F%282%29 or x+=+%28-8+-+4%29%2F%282%29 Break up the expression.


x+=+%28-4%29%2F%282%29 or x+=++%28-12%29%2F%282%29 Combine like terms.


x+=+-2 or x+=+-6 Simplify.


So the answers are x+=+-2 or x+=+-6