SOLUTION: Please help me solve this expression? Complete the square. {{{x^2-10x+24=0}}}

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Question 102618: Please help me solve this expression? Complete the square. x%5E2-10x%2B24=0
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-10x%2B24=0
x^2-10x =-24 subtract 24 from each side.
x^2-10x+25=25-24 take 1/2 of -10 and square it.
(x-5)^2=1 factor the left side.
x-5=+-1 take sqrt of both sides
x=5+-1
x=6, x=4
Ed

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-10x%2B24=0 Start with the given equation


x%5E2-10x=-24 Subtract 24 from both sides


Take half of the x coefficient -10 to get -5 (ie -10%2F2=-5)
Now square -5 to get 25 (ie %28-5%29%5E2=25)



x%5E2-10x%2B25=-24%2B25 Add this result (25) to both sides. Now the expression x%5E2-10x%2B25 is a perfect square trinomial.




%28x-5%29%5E2=-24%2B25 Factor x%5E2-10x%2B25 into %28x-5%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-5%29%5E2=1 Combine like terms on the right side

x-5=0%2B-sqrt%281%29 Take the square root of both sides

x=5%2B-sqrt%281%29 Add 5 to both sides to isolate x.

So the expression breaks down to
x=5%2Bsqrt%281%29 or x=5-sqrt%281%29


x=5%2B1 or x=5-1 Take the square root of 1 to get 1


x=6 or x=4 Now combine like terms

So our answer is
x=6 or x=4


Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-10x%2B24%29+ graph of y=x%5E2-10x%2B24

Here we can see that the x-intercepts are x=6 and x=4, so this verifies our answer.