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Given 8x² - 48x = -104, rewrite the equation with a coefficient of 1: x² - 6x = -13.

Complete the square: x² - 6x + 9 = -13 + 9.
Factor the trinomial and simplify: (x - 3)² = -4.

1 Answer

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The solution to the quadratic equation by completing the square is:

x = 3 ± √-4

How to complete the square?

We are given the quadratic equation as:

8x² - 48x = -104

Divide through y 8 to get:

x² - 6x = -13

Add half of the square of the coefficient of x to both sides to get:

x² - 6x + (-6/2)² = -13 + (-6/2)²

x² - 6x + 9 = -13 + 9

Factoring the left gives:

(x - 3)² = -4

Take the square root of both sides too get:

x - 3 = √-4

x = 3 ± √-4