The quadratic equation that has the same solutions as the given equation. is (x - 5)² = 36
Since we have the quadratic equation x² - 10x - 11 = 0.
To determine the equation that has thye same solution as the given equation, we solve the equation by completing the square method.
To complete the square, we add the square of half the coefficient of x to both sides of the equation.
So, we have x² - 10x - 11 = 0
We then add the square of half the coefficient of x to both sides.
So, we have
x² - 10x - 11 + (-10/2)² = 0 + (-10/2)²
x² - 10x - 11 + (-5)² = 0 + (-5)²
Next, we simplify, thus
x² - 10x - 11 + 5² = 0 + 5²
x² - 10x + 5² - 11 = 0 + 5²
(x - 5)² - 11 = 25 [since (x² - 10x + 5² = (x - 5)²]
(x - 5)² = 25 + 11
(x - 5)² = 36
So, the quadratic equation that has the same solutions as the given equation. is (x - 5)² = 36
Learn more about completing the square here:
brainly.com/question/26107616
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