Questions: Solve this equation by Factoring. (6 points) x^2+x-12=0

Solution Steps

To solve the quadratic equation \(x^2 + x - 12 = 0\) by factoring, we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(1\) (the coefficient of the linear term). Once we identify these numbers, we can express the quadratic as a product of two binomials and solve for \(x\).

We start with the equation \(x^2 + x - 12 = 0\). To factor this quadratic, we look for two numbers that multiply to \(-12\) and add to \(1\). The numbers \(-3\) and \(4\) satisfy these conditions. Thus, we can factor the equation as: \[ (x - 3)(x + 4) = 0 \]

Next, we set each factor equal to zero to find the solutions for \(x\):

1. \(x - 3 = 0\)
2. \(x + 4 = 0\)

Solving these equations gives us:

1. From \(x - 3 = 0\), we find \(x = 3\).
2. From \(x + 4 = 0\), we find \(x = -4\).

Final Answer