SOLUTION: {{{ g(x)=(x+5)^2 }}}, find all values of x for which g(x)=15

Algebra ->  Functions -> SOLUTION: {{{ g(x)=(x+5)^2 }}}, find all values of x for which g(x)=15      Log On


   

Question 692538: +g%28x%29=%28x%2B5%29%5E2+, find all values of x for which g(x)=15
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
+g%28x%29+=+15+
+%28x%2B5%29%5E2+=+15+
+%28x%2B5%29%28x%2B5%29+=+15+
+%28x%29%28x%29+%2B+5x+%2B+5x+%2B+%285%29%285%29+=+15+
+x%5E2+%2B+10x+%2B+25+=+15+
+x%5E2+%2B+10x+%2B+10+=+0+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B10+=+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=%2810%29%5E2-4%2A1%2A10=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+60+%29%29%2F2%5C1+=+-1.12701665379258
x%5B2%5D+=+%28-%2810%29-sqrt%28+60+%29%29%2F2%5C1+=+-8.87298334620742

Quadratic expression 1x%5E2%2B10x%2B10 can be factored:
1x%5E2%2B10x%2B10+=+1%28x--1.12701665379258%29%2A%28x--8.87298334620742%29
Again, the answer is: -1.12701665379258, -8.87298334620742. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B10+%29