7m² + 24m - 2 = m² - 9 Algebra Help?

Question

Please solve by using the "completing the square method," as well as showing the work. I do not understand this, and really need help on it! Thanks!

Answer 1

Completing the square Method :

The equation is 7m² + 24m - 2 = m² - 9.

Separate variables and constants aside.

Subtracting m² from each side.

7m² + 24m - 2 - m² = m² - 9 - m².

6m² + 24m - 2 = - 9.

Add 2 to each side.

6m² + 24m - 2 + 2 = - 9 + 2

6m² + 24m = - 7

Divide each side by 6.

(6m²)/6 + (24m)/6 = - 7/6

m² + 4m = - 7/6

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 4. So, (half the x coefficient)² = (4/2)²= 4.

Add 4 to each side.

m² + 4m + 4 = - 7/6 + 4

(m + 2)² = [-7+6(4)]/6

(m + 2)² = 17/6

m + 2 = ± √(17/6)

m = - 2 ± √(17/6).

The value of m = - 2 + √(17/6) and m = - 2 - √(17/6).