To solve the equation \(0 = x^2 - 6x - 20\), we can either factor it, complete the square, or use the quadratic formula. Here, we will factor it.
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Factoring the equation: We need to find two numbers that multiply to \(-20\) (the constant term) and add to \(-6\) (the coefficient of \(x\)). These numbers are \(-10\) and \(+4\).
So, we can factor the quadratic as: \[ 0 = (x - 10)(x + 4) \]
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Setting each factor to zero: We set each factor equal to zero to find the solutions for \(x\). \[ x - 10 = 0 \quad \text{or} \quad x + 4 = 0 \]
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Solving for \(x\):
- From \(x - 10 = 0\), we get: \[ x = 10 \]
- From \(x + 4 = 0\), we get: \[ x = -4 \]
Thus, the solutions to the equation \(0 = x^2 - 6x - 20\) are:
- \(x = 10\)
- \(x = -4\)
If you are looking for a specific format for the numbered list, please clarify what you need for points 1, 2, and 3, and I can adjust accordingly!