Questions: QUESTION 21 - 1 POINT Solve the following quadratic by factoring. x^2+x-42=0 List the answers separated by a comma. For example, if you found solutions x=1 and x=2, you would enter 1, 2. Provide your answer below: x=

QUESTION 21 - 1 POINT Solve the following quadratic by factoring. x^2+x-42=0

List the answers separated by a comma. For example, if you found solutions x=1 and x=2, you would enter 1, 2.

Provide your answer below: x=

Transcript text: QUESTION 21 - 1 POINT Solve the following quadratic by factoring. \[ x^{2}+x-42=0 \] List the answers separated by a comma. For example, if you found solutions $\boldsymbol{x}=\mathbf{1}$ and $\boldsymbol{x}=\mathbf{2}$, you would enter $\mathbf{1}, \mathbf{2}$. Provide your answer below: \[ x= \] $\square$

Solution

Solution Steps

To solve the quadratic equation $x^2 + x - 42 = 0$ by factoring, we need to find two numbers that multiply to $-42$ and add to $1$. Once these numbers are identified, we can express the quadratic as a product of two binomials and solve for $x$.

Step 1: Identify the Quadratic Equation

We start with the quadratic equation: \[ x^2 + x - 42 = 0 \]

Step 2: Factor the Quadratic Equation

To factor the quadratic equation, we need to find two numbers that multiply to $-42$ and add to $1$. These numbers are $-7$ and $6$. Thus, we can express the quadratic as: \[ (x - 7)(x + 6) = 0 \]

Step 3: Solve for $x$

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