Question

Solve the equation by the square root property.



(x - 6)2 = -6

Answer 1

`\displaystyle{x = 6 \pm √(6) i}`

Explanation:

Given the equation:

`\displaystyle{ {(x - 6)}^(2) = - 6}`

Square root both sides:

`\displaystyle{ \sqrt{ {(x - 6)}^(2) } = √( - 6) } \\ \\ \displaystyle{x - 6 = \pm √(6) i}`

From the step above, we cancel the square root from the left side. For the right side, we convert the square root of negative to i through the definition below. When solving quadratic equation using the square root method, we have to add plus-minus all time.

`\displaystyle{i = √( - 1) }`

Solve for x by adding both sides by 6, which results in:

`\displaystyle{x = 6 \pm √(6) i}`