Question

Solve 6x²−10x=−50 by completing the square

Answer 1

The solutions to the quadratic equation using completing the square method are 5/6 - [(5i/6)√11]/6 and 5/6 + [(5i/6)√11]/6.

What are the solution(s) to the given quadratic equation?

Given the equation in the question;

6x² − 10x = −50

Using completing the square method

First, divide each term by the coefficient of x²

6x²/6 − 10x/6 = −50/6

x² − 10x/6 = −50/6

Now, we take the half of the coefficient of x and square it.

(-10/6 ÷ 2)² = (-10/12)² = 25/36

Now we add 25/36 to both sides

x² − 10x/6 + 25/36 = −50/6 + 25/36

Next, we rewrite as a perfect square on the left.

( x - 5/6)² = −50/6 + 25/36

( x - 5/6)² = −275/36

Take square root of both sides

x - 5/6 = ±[√( (5i/6)² × 11 )]/6

x - 5/6 = ±[ (5i/6)√11 ]/6

x  = 5/6 ± [ (5i/6)√11 ]/6

x = 5/6 - [(5i/6)√11]/6, 5/6 + [(5i/6)√11]/6

The solutions to the quadratic equation using completing the square method are 5/6 - [(5i/6)√11]/6 and 5/6 + [(5i/6)√11]/6.

Learn more about solving quadratic equation using completing the square here: brainly.com/question/12356597

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