Question

Which of the following is a solution of x2 + 6x = −18? x = 3 − 3i x = −3 + 3i x = −6 + 3i x = 6 − 3i

Answer 1

x=-3+3i

Explanation:

since it could either be x=-3+3i or x=-3-3i. the answer only allows for x=-3+3i then that is your answer.

Answer 2

Step 1 ) Move all terms right side of the equation.

`\displaystyle\ x^(2) + 6x = -18`

`\displaystyle\ x^(2) + 6x + 18 = -18 + 18`

`\displaystyle\ x^(2) +6x + 18 = 0`

Step 2 ) Apply quadratic formula. (Note: There are 2 solutions)

`\displaystyle\ x^(2) +6x + 18 = 0`

`\displaystyle\ x = \frac{-b\sqrt{b^(2)-4ac}}{2a}, \displaystyle\ x = \frac{-b-\sqrt{b^(2)-4ac}}{2a}`

`\displaystyle\ x = \frac{-6+\sqrt{6^(2)-4 * 18}}{2} , \displaystyle\ x = \frac{-6-\sqrt{6^(2)-4*18}}{2}`

`\displaystyle\ x = (-6+6i)/(2)` ,

`\displaystyle\ x = (-6-6i)/(2)`

Step 3 ) Simplify.

`\displaystyle\ x = (-6+6i)/(2)` ,

`\displaystyle\ x = (-6-6i)/(2)`

`\displaystyle\ x = -3+ 3i`,

`\displaystyle\ x = -3 - 3i`

Since the options only provide one of the answer we found, the answer is...

`\displaystyle\ x = -3 - 3i`

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- Marlon Nunez