solve each of the folowing equations by factoring and show your work
x²+x²=13x²-36
To solve the equation x² + x² = 13x² - 36 by factoring, we first combine like terms on both sides of the equation:
2x² = 13x² - 36
Next, we move all terms to one side of the equation to set it equal to zero:
0 = 13x² - 2x² - 36
Simplifying the equation gives us:
0 = 11x² - 36
Now, let's factor the quadratic equation:
To determine the factors, we need to consider two numbers that:
1. Multiply to give the product of the constant term (-36 in this case) and
2. Add up to give the coefficient of the x term (-11 in this case).
By trial and error, we can find that the factors of -36 that add up to -11 are -12 and 3.
So, we can rewrite the equation as:
0 = (11x + 3)(x - 12)
Now, we can set each factor equal to zero and solve for x:
11x + 3 = 0 and x - 12 = 0
Solving the first equation gives us:
11x = -3
x = -3/11
Solving the second equation gives us:
x = 12
Therefore, the solutions to the quadratic equation x² + x² = 13x² - 36 are x = -3/11 and x = 12.