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Complete the square to solve the following quadratic equation: x2−6x−20=20 .(1 point) Responses x=3+210−−√, 3−210−−√ x equals 3 plus 2 Start Root 10 End Root comma 3 minus 2 Start Root 10 End Root x=52, x=−46 x equals 52 , x equals negative 46 x=10, x=−4 x equals 10 , x equals negative 4 x=−10, x=4

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To complete the square for the equation \(x^2 - 6x - 20 = 20\), start by rewriting the equation:

  1. Move \(20\) to the right side: \[ x^2 - 6x - 20 - 20 = 0 \implies x^2 - 6x - 40 = 0 \]

  2. Add \(40\) to both sides: \[ x^2 - 6x = 40 \]

  3. To complete the square, take half of the coefficient of \(x\) (which is \(-6\)), square it, and add it to both sides. Half of \(-6\) is \(-3\) and squaring that gives \(9\): \[ x^2 - 6x + 9 = 40 + 9 \] \[ x^2 - 6x + 9 = 49 \]

  4. Now the left side factors to: \[ (x - 3)^2 = 49 \]

  5. Take the square root of both sides: \[ x - 3 = 7 \quad \text{or} \quad x - 3 = -7 \]

  6. Solve for \(x\): \[ x = 10 \quad \text{or} \quad x = -4 \]

Thus, the solutions are: \[ x = 10, \quad x = -4 \]

The answer is:

  • \(x = 10, x = -4\)