SOLUTION: x^2 + 14x+ 24 =0 ok so x^2 + 14x = -24 then my book says x^2 + 14x +49= 25 how did my text book get the 49? then it continues (x + 7)^2 =25 x +7 = +-5 x=-7 +-5

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Question 183951: x^2 + 14x+ 24 =0
ok so x^2 + 14x = -24
then my book says x^2 + 14x +49= 25 how did my text book get the 49?

then it continues (x + 7)^2 =25

x +7 = +-5
x=-7 +-5
so x= -2 or -12 i know how my book got the answer but not sure how my book got the 49 before(x+7)^2=25
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
x^2 + 14x+ 24 =0
Your book was solving it by completing the square like this:
x^2+14x =-24
x^2+14x+49=-24+49 divide the 2nd term by 2 and square the result 49 and use it as the 3rd term and add 49 to the other side to keep everything equal.
(x+7)^2=25
x+7=+-5 sqrt of each side.
x=-7+-5
x=-12, x=-2
You can also get the same answer by factoring or using the quadratic formula.
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Ed
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Factoring is easiest:
(x+12)(x+2)=0
x=-2, x=-12
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Quadratic equation:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -2, -12. Here's your graph: