SOLUTION: Give exact and approximate solutions to three decimal places (x-6)^2=18

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Question 471368: Give exact and approximate solutions to three decimal places
(x-6)^2=18
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
(x-6)2=18
x2-12x+36=18
x2-12x+18=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B18+=+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=%28-12%29%5E2-4%2A1%2A18=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+72+%29%29%2F2%5C1+=+10.2426406871193
x%5B2%5D+=+%28-%28-12%29-sqrt%28+72+%29%29%2F2%5C1+=+1.75735931288072

Quadratic expression 1x%5E2%2B-12x%2B18 can be factored:
1x%5E2%2B-12x%2B18+=+1%28x-10.2426406871193%29%2A%28x-1.75735931288072%29
Again, the answer is: 10.2426406871193, 1.75735931288072. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B18+%29
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