Questions: x^2 = 5x + 14

x^2 = 5x + 14
Transcript text: $x^{2}=5 x+14$
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Solution

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Solution Steps

Step 1: Rearranging the Equation

We start with the equation

\[ x^{2} = 5x + 14 \]

To bring all terms to one side, we rearrange it to the standard polynomial form:

\[ x^{2} - 5x - 14 = 0 \]

Step 2: Factoring the Polynomial

Next, we factor the polynomial \( x^{2} - 5x - 14 \). The factorization yields:

\[ (x - 7)(x + 2) = 0 \]

Step 3: Finding the Roots

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

  1. \( x - 7 = 0 \) leads to \( x = 7 \)
  2. \( x + 2 = 0 \) leads to \( x = -2 \)

Thus, the solutions to the equation \( x^{2} = 5x + 14 \) are \( x = 7 \) and \( x = -2 \).

Final Answer

\(\boxed{x = 7}\) and \(\boxed{x = -2}\)

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