Solve x² = 12x - 15 by completing the square. What is the solution set of the equation?

Solution:

It is given that

x² = 12x - 15

We can write it as

x² - 12x = -15

Let us complete the square by adding (-b/2)² on both sides of the equation

x² - 12x + (-12/2)² = -15 + (-12/2)²

We get

x² - 12x + (-6)² = -15 + (-6)²

x² - 12x + 36 = -15 + 36

(x - 6)² = 21

Taking square root on both sides

x - 6 = ± √21

x - 6 = √21 and x - 6 = - √21

x = 6 + √21 and x = 6 - √21

Therefore, the solution set of the equation is x = 6 + √21 and x = 6 - √21.

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Solve x² = 12x - 15 by completing the square. What is the solution set of the equation?

Summary:

Solving x² = 12x - 15 by completing the square the solution set of the equation is x = 6 + √21 and x = 6 - √21.