Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying \( x \)-intercepts. \[ x^{2}-x-12=0 \]

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). The two numbers that meet these criteria are -4 and 3. Therefore, we can factor the equation as follows: \[ (x - 4)(x + 3) = 0 \] Now, we can set each factor to zero to find the values of \( x \): 1. \( x - 4 = 0 \) ⟹ \( x = 4 \) 2. \( x + 3 = 0 \) ⟹ \( x = -3 \) So, the solutions to the equation \( x^{2}-x-12=0 \) are \( x = 4 \) and \( x = -3 \). To check our solutions, we can substitute these values back into the original equation: For \( x = 4 \): \[ 4^2 - 4 - 12 = 16 - 4 - 12 = 0 \] For \( x = -3 \): \[ (-3)^2 - (-3) - 12 = 9 + 3 - 12 = 0 \] Both solutions satisfy the equation! Now, if you prefer a graphical method, you could graph \( y = x^2 - x - 12 \). The \( x \)-intercepts (where the graph crosses the x-axis) should correspond to the solutions we found, which are indeed \( x = 4 \) and \( x = -3 \).