Questions: Use factoring to solve the quadratic equation x^2 - x - 72 = 0 The solution set is

Transcript text: Use factoring to solve the quadratic equation \[ x^{2}-x-72=0 \] The solution set is $\square$

Solution

Solution Steps

To solve the quadratic equation $x^2 - x - 72 = 0$ by factoring, we need to find two numbers that multiply to $-72$ and add to $-1$. Once we identify these numbers, we can express the quadratic as a product of two binomials and solve for $x$.

Step 1: Identify the Quadratic Equation

The given quadratic equation is: \[ x^2 - x - 72 = 0 \]

Step 2: Factor the Quadratic Equation

To factor the quadratic equation, we need to find two numbers that multiply to $-72$ and add to $-1$. These numbers are $-9$ and $8$. Thus, the equation can be factored as: \[ (x - 9)(x + 8) = 0 \]

Step 3: Solve for $x$

Set each factor equal to zero and solve for $x$: