To solve the quadratic equation \(0 = x^2 - 6x - 20\), we can use the factoring method or the quadratic formula.
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Factoring the Equation: First, we need to express the quadratic in factored form. We look for two numbers that multiply to \(-20\) (the constant term) and add to \(-6\) (the coefficient of \(x\)).
The numbers that satisfy these conditions are \(-10\) and \(+4\), since \(-10 \times 4 = -40\) and \(-10 + 4 = -6\). Therefore, we can factor the equation as follows:
\[ 0 = (x - 10)(x + 4) \]
Setting each factor equal to zero gives us the solutions:
\[ x - 10 = 0 \quad \Rightarrow \quad x = 10 \]
\[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \]
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Solutions: The solutions to the equation \(0 = x^2 - 6x - 20\) are:
- \(x = 10\)
- \(x = -4\)
If you need any further steps or clarifications, feel free to ask!