Question
Solve for all values of x by factoring
X^2+6x-12=4
X^2+6x-12=4
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Answered by
GPT 3.5
To solve this equation by factoring, we first rearrange it to be in the form: x^2 + 6x - 16 = 0.
Then, we need to find two numbers whose product is -16 and whose sum is 6.
The numbers that satisfy this condition are 8 and -2.
So, we can rewrite the equation as: (x + 8)(x - 2) = 0.
Now, we can set each factor equal to zero and solve for x:
x + 8 = 0 -> x = -8
x - 2 = 0 -> x = 2
Therefore, the solution to the equation x^2 + 6x - 16 = 0 is x = -8, 2.
Then, we need to find two numbers whose product is -16 and whose sum is 6.
The numbers that satisfy this condition are 8 and -2.
So, we can rewrite the equation as: (x + 8)(x - 2) = 0.
Now, we can set each factor equal to zero and solve for x:
x + 8 = 0 -> x = -8
x - 2 = 0 -> x = 2
Therefore, the solution to the equation x^2 + 6x - 16 = 0 is x = -8, 2.
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