solve by completing the square

Question

3 divide (r-1)(r+2)=1.

Answer 1

Assume the expression is .

The above equation can form quadratic equation .

Quadratic formula

Where a = 1, b = 1 and c = - 5.

.

Comments

The roots are r = (√21 - 1)/2 and r = (- √21 - 1)/2.

Answer 2

The equation is .

Separate variables and constants aside by adding 2 to each side.

r ² + r = 3 + 2

r ² + r = 5.

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

 Here r coefficient = 1. so, (half the r coefficient)² = (1/2)²= 1/4.

Add 1/4 to each side.

r ² + r + 1/4 = 5 + 1/4

(r + 1/2)² = (20 + 1)/4

(r + 1/2)² = (21)/4

(r + 1/2)² = (± √21/2)²

r + 1/2 = ± √21/2

r = - 1/2 + √21/2 and r = - 1/2 - √21/2.

The roots are r = (√21 - 1)/2 and r = (- √21 - 1)/2.