Questions: Solve the equation by factoring. x^2 = 4x + 21

Transcript text: Solve the equation by factoring. \[ x^{2}=4 x+21 \]

Solution

Solution Steps

Step 1: Rewrite the Equation in Standard Form

First, we rewrite the given equation \(x^2 = 4x + 21\) in standard form by moving all terms to one side: \[ x^2 - 4x - 21 = 0 \]

Step 2: Factor the Quadratic Expression

Next, we factor the quadratic expression \(x^2 - 4x - 21\): \[ x^2 - 4x - 21 = (x - 7)(x + 3) \]

Step 3: Solve for the Roots

To find the roots, we set each factor equal to zero and solve for \(x\): \[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \] \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \]

Final Answer

The solutions to the equation \(x^2 = 4x + 21\) are: \[ \boxed{x = 7 \text{ or } x = -3} \]

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