how to solve a quadratic equation with completing the square

Question

a^+2a-3=0

Answer 1

a² + 2a - 3 = 0

 

Rewrite the equation as a² + 2a = 3

 

Take half of the coefficient of 2a and square that number:

             (½(2))² = 1² = 1

 

Add 1 to both sides of the equation:

 

             a² + 2a + 1 = 3 + 1

 

             a² + 2a + 1 = 4

 

Factor the left hand side and solve for a:

 

             (a + 1)² = 4       a + 1 = ±√4

 

                                               a = -1 ± 2 = 1, -3

Answer 2

a² + 2a - 3 = 0

 

First, add 3 to both sides:

 

a² - 2a = 3

 

To complete the square, take one-half of the coefficient of the a term (2) and square it ((2/2)²) and add it to both sides of the equation.

 

a² + 2a + (2/2)² = 3 + (2/2)²

 

a² + 2a + 1 = 4

 

(a + 1)² = 4

 

√(a+1)² = √4

 

a + 1 = ±2

 

a = -3, 1