SOLUTION: Please help me solve : nine less than the square of a number is the same as twice the number. find the number

Algebra ->  Expressions-with-variables -> SOLUTION: Please help me solve : nine less than the square of a number is the same as twice the number. find the number       Log On


   

Question 522941: Please help me solve :
nine less than the square of a number is the same as twice the number. find the number
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2-9+=+2x+
+x%5E2+-2x+-9+=+0+
.
+graph%28500%2C500%2C-10%2C10%2C-20%2C20%2Cx%5E2-2%2Ax-9%29+
.
complete the square
.
+x%5E2+-2x+%2B1+=+9+%2B1+
.
+%28x-1%29%5E2+=+10+
+%28x-1%29+=+sqrt%2810%29+
.
+sqrt%2810%29+=+3.16227766016838+
.
Remember the sqrt is plus or minus.
.
+x+-1+=+-3.16227766016838+
+x+=+-2.16227766016838+
.
+x-1+=+3.16227766016838+
+x+=+4.16227766016838+
.
OR
.
You could have used the quadratic equation.
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-9+=+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=%28-2%29%5E2-4%2A1%2A-9=40.

Discriminant d=40 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+40+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+4.16227766016838
x%5B2%5D+=+%28-%28-2%29-sqrt%28+40+%29%29%2F2%5C1+=+-2.16227766016838

Quadratic expression 1x%5E2%2B-2x%2B-9 can be factored:
1x%5E2%2B-2x%2B-9+=+1%28x-4.16227766016838%29%2A%28x--2.16227766016838%29
Again, the answer is: 4.16227766016838, -2.16227766016838. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-9+%29