Question

Which of the following are solutions to the equation below?

Check all that apply.
x^2-2x-24=0 A. 6
B. 4
C.-6
D.-24
E. -4

Answer 1

`\boxed{A. \: 6 \: \: \: and \: \: \: E. \: -4}`

Explanation:

`= > {x}^(2) - 2x - 24 = 0 \\ \\ = > {x}^(2) - (6 - 4)x - 24 = 0 \\ \\ = > {x}^(2) - 6x + 4x - 24 = 0 \\ \\ = > x(x - 6) + 4(x - 6) = 0 \\ \\ = > (x - 6)(x + 4) = 0 \\ \\ = > x - 6 = 0 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x + 4 = 0 \\ \\ = > x = 6 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: x = - 4`

Answer 2

A. 6

E. -4

Explanation:

x² - 2x - 24 = 0

x - 6

x 4

(x - 6)(x + 4) = 0

Set each parenthesis equal to 0:

(x - 6) = 0

Isolate the variable, x. Add 6 to both sides;

x - 6 (+6) = 0 (+6)

x = 0 + 6

x = 6

(x + 4) = 0

Isolate the variable, x. Subtract 4 from both sides:

x + 4 (-4) = 0 (-4)

x = 0 - 4

x = -4

x = -4, 6 are your solutions, or A. & E.

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