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.
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: https://brainly.com/question/12356597
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