Questions: Quadratic Equations Quadratic Functions Solve the equation by factoring. x^2+9x=10 x=[?],

Quadratic Equations Quadratic Functions Solve the equation by factoring. x^2+9x=10 x=[?],
Transcript text: Quadratic Equations Quadratic Functions Solve the equation by factoring. \[ \begin{array}{l} x^{2}+9 x=10 \\ x=[?], \end{array} \]
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Solution

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Solution Steps

Step 1: Rewrite the Equation

We start with the quadratic equation given in the problem: \[ x^2 + 9x = 10 \] Rearranging this equation gives us: \[ x^2 + 9x - 10 = 0 \]

Step 2: Factor the Polynomial

Next, we factor the polynomial \(x^2 + 9x - 10\). The factorization results in: \[ (x - 1)(x + 10) = 0 \]

Step 3: Find the Roots

To find the roots of the equation, we set each factor equal to zero:

  1. \(x - 1 = 0 \implies x = 1\)
  2. \(x + 10 = 0 \implies x = -10\)

Final Answer

The solutions to the equation are: \[ \boxed{x = 1} \quad \text{and} \quad \boxed{x = -10} \]

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