Questions: Solve the quadratic equation by factoring. x^2 + 2x = 48

Transcript text: Solve the quadratic equation by factoring. \[ x^{2}+2 x=48 \]

Solution

Solution Steps

To solve the quadratic equation by factoring, first rewrite the equation in the standard form \( ax^2 + bx + c = 0 \). Then, factor the quadratic expression into two binomials. Finally, use the zero product property to find the values of \( x \).

Step 1: Rewrite the Equation

Start by rewriting the given quadratic equation in standard form: \[ x^2 + 2x - 48 = 0 \]

Step 2: Factor the Quadratic Expression

Factor the quadratic expression \(x^2 + 2x - 48\) into two binomials: \[ (x - 6)(x + 8) = 0 \]

Step 3: Apply the Zero Product Property

Use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero and solve for \(x\): \[ x - 6 = 0 \quad \text{or} \quad x + 8 = 0 \]

Step 4: Solve for \(x\)

Solving these equations gives: \[ x = 6 \quad \text{or} \quad x = -8 \]