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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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       Log On


   



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) About Me  (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.
.
Ed
.
Factoring is easiest:
(x+12)(x+2)=0
x=-2, x=-12
.
Quadratic equation:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B14x%2B24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2814%29%5E2-4%2A1%2A24=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2814%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+-2
x%5B2%5D+=+%28-%2814%29-sqrt%28+100+%29%29%2F2%5C1+=+-12

Quadratic expression 1x%5E2%2B14x%2B24 can be factored:
1x%5E2%2B14x%2B24+=+%28x--2%29%2A%28x--12%29
Again, the answer is: -2, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B14%2Ax%2B24+%29