Question

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation? (negative 6 minus StartRoot 51 EndRoot comma negative 6 + StartRoot 51 EndRoot) (negative 6 minus StartRoot 21 EndRoot comma negative 6 + StartRoot 21 EndRoot) (6 minus StartRoot 51 EndRoot comma 6 + StartRoot 51 EndRoot) (6 minus StartRoot 21 EndRoot comma 6 + StartRoot 21 EndRoot)

Answer 1

LAST OPTION:
`(6-√(21),6+√(21))`

Explanation:

1. Subtract
`12x` from both sides of the equation:

`x^2-12x= 12x- 15-12x\\\\x^2-12x=-15`

2. Since
`b=12`:

`((b)/(2))^2=((12)/(2))^2=(6)^2`

3. Now can complete the square. Add
`(6)^2` to both sides of the equation:

`x^2-12x+6^2=-15+6^2`

4. Simplifying:

`(x-6)^2=21`

5. Solve for "x":

`√((x-6)^2)=\±√(21)\\\\x-6=\±√(21)\\\\x=6\±√(21)\\\\x_1=6+√(21)\\\\x_2=6-√(21)`

6. The solution set is:

`(6-√(21),6+√(21))`