Solve this equation by completing the square: x2 + 4x - 13 = - 8

x = 1 or x = - 5

Step-by-step explanation:

We are given;

The quadratic equation, x² + 4x - 13 = - 8

We are required to solve the equation using the completing square method.

To do this, we use the following steps;

Step 1: We make sure the coefficient of x² is one

x² + 4x - 13 = - 8

Step 2: Combine the like terms (take the constant term to the other side)

x² + 4x - 13 = - 8

x² + 4x = - 8 + 13

we get

x² + 4x = 5

Step 3: We add the square of half the coefficient of x on both sides of the equation

Coefficient of x = 4

Half of coefficient of x = 2

Square of half the coefficient of x = 2² (4)

We get;

x² + 4x + (2²) = 5 + (2²)

Step 4: Put x and 2 under one square and the solve the other side of the equation.

We get

(x + 2) ² = 5 + 4

(x + 2) ² = 9

Step 5: Get the square root on both sides of the equation;

(x + 2) ² = 9

√ (x + 2) ² = ±√9

(x + 2) = ±3

Therefore;

x+2 = + 3 or x + 2 = - 3

Thus, x = 1 or - 5

The solution of the equation is x = 1 or x = - 5