Solve the equation by factoring: 4x² + 9x − 9 = 0
To solve this quadratic equation by factoring, we need to find two numbers that multiply to -36 (4 * -9) and add up to 9.
The two numbers that meet these criteria are 12 and -3, as 12 * -3 = -36 and 12 + (-3) = 9.
Therefore, we rewrite the equation as:
4x² + 12x − 3x − 9 = 0
Factor by grouping:
4x(x + 3) - 3(x + 3) = 0
Factor out the common factor:
(4x - 3)(x + 3) = 0
Set each factor equal to zero:
4x - 3 = 0 or x + 3 = 0
Solve for x:
4x = 3
x = 3/4
x = -3
Therefore, the solutions to the equation 4x² + 9x − 9 = 0 are x = 3/4 and x = -3.