Complete the square to solve the equation below x^2 + 10x - 13 = 17

See below in exact form

or

2.42, - 12.42 to the nearest hundredth.

Step-by-step explanation:

x^2 + 10x - 13 = 17

(x + 5) ^2 - 25 - 13 = 17

(x + 5) ^2 = 17 + 38 = 55

x + 5 = + / - √55

x = - 5 + √55, - 5 - √55.

x = - 12.42 or x = 2.42

Step-by-step explanation:

x^2 + 10x - 13 = 17

To solve this using the completing the square method, we will follow the steps below;

First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation

x^2 + 10x - 13 + 13 = 17 + 13

x^2 + 10x = 30

The next step is to add both-side of the equation by square of half of the coefficient of x (that is; half of 10 is 5, then we will add 5² to both-side of the equation)

x^2 + 10x + 5² = 30 + 5²

Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation

(x + 5) ² = 30 + 25

(x + 5) ² = 55

We will then take the square root of both-side of the equation

√ (x + 5) ² = ±√55

x + 5 = ±√55

To get the value of x, we will subtract 5 from both-side of the equation

x + 5 - 5 = ±√55 - 5

x = ±√55 - 5

Either x = + √55 - 5 = 7.42 - 5 = 2.42

OR

x = - √55 - 5 = - 7.42 - 5 = - 12.42

Therefore either x = - 12.42 or x = 2.42

x = - 12.42 or 2.42