Questions: Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying (x)-intercepts. [ x^2-x-72=0 ] The solution set is (square)

Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying (x)-intercepts.

[ x^2-x-72=0 ]

The solution set is (square)

Transcript text: Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying $x$-intercepts. \[ x^{2}-x-72=0 \] The solution set is $\square$

Solution

Solution Steps

Step 1: Identify the Quadratic Equation

The given quadratic equation is $ x^2 + (-1)x + (-72) = 0 $.

Step 2: Factor the Quadratic Equation

To factor the equation, we find two numbers $m$ and $n$ such that $m + n = -1$ and $m \cdot n = -72$. After calculation, we find that $m = 9$ and $n = -8$, so the factored form of the equation is $(x - 9)(x + 8) = 0$.

Step 3: Solve for $x$

Setting each factor equal to zero gives us the solutions $x = 9$ and $x = -8$.

Step 4: Verification

To verify the solutions, substitute them back into the original equation or use a graphing utility. If the solutions are correct, they will satisfy the original equation or correspond to the $x$-intercepts on the graph.