Solve the equation x² + 6x = -11/4

A.) x = -3 and 2

B.) x = -2 and 3

C.) x = 1/2 and -11/2

D.) x = -1/2 and -11/2

A.) x = -3 and 2

B.) x = -2 and 3

C.) x = 1/2 and -11/2

D.) x = -1/2 and -11/2

Nobody ever likes completing the square, so we'll go with that method!

x² + 6x = -11/4

x² + 6x + 9 = (-11/4) + 9 {took half of coefficient of x, squared it, and added to each side....that completes the square}

(x + 3)² = 25/4 {factored the left side and added -11/4 and 9}

x + 3 = ±5/2 {took square root of each side}

x = -3 ± (5/2) {subtracted 3 from each side}

x = (-6/2) ± (5/2) {got common denominator}

x = -1/2 or -11/2 {added and subtracted, using the ± sign}

x² + 6x = -11/4

x² + 6x + 9 = (-11/4) + 9 {took half of coefficient of x, squared it, and added to each side....that completes the square}

(x + 3)² = 25/4 {factored the left side and added -11/4 and 9}

x + 3 = ±5/2 {took square root of each side}

x = -3 ± (5/2) {subtracted 3 from each side}

x = (-6/2) ± (5/2) {got common denominator}

x = -1/2 or -11/2 {added and subtracted, using the ± sign}

**D.) x = -1/2 and -11/2****Ask Algebra House**