Answer: the solutions to the equation -13x^2 + 4 = x^2 - 8 are:
A. x = -3 and x = 1
Step-by-step explanation: To find the solutions to the equation -13x^2 + 4 = x^2 - 8, we need to set the equation equal to 0 and solve for x.
-13x^2 + 4 = x^2 - 8
First, let's move all the terms to one side to get a quadratic equation in standard form:
-13x^2 - x^2 + 4 + 8 = 0
-14x^2 + 12 = 0
Next, let's solve the quadratic equation. We can use factoring or the quadratic formula. In this case, let's use factoring:
-14x^2 + 12 = 0
-2(7x^2 - 6) = 0
Now, we can set each factor equal to 0:
-2 = 0 (This is not possible, so we can ignore it.)
7x^2 - 6 = 0
Next, let's solve for x by factoring again:
7x^2 - 6 = 0
(7x - 3)(x + 2) = 0
Now, we can set each factor equal to 0 and solve for x:
7x - 3 = 0
7x = 3
x = 3/7
x + 2 = 0
x = -2