Question

If using the method of completing the square to solve the quadratic equation x^2-10x-13=0, which number would have to be added to "complete the square"?

Answer 1

Answer: The solution to the problem is based on the solutions

from the subproblems.

x = {8.464101615, 1.535898385}

Step-by-step explanation:  

x^2-10x+13=0

Simplifying

x2 + -10x + 13 = 0

Reorder the terms:

13 + -10x + x2 = 0

Solving

13 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.

13 + -10x + -13 + x2 = 0 + -13

Reorder the terms:

13 + -13 + -10x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0

0 + -10x + x2 = 0 + -13

-10x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13

-10x + x2 = -13

The x term is -10x.  Take half its coefficient (-5).

Square it (25) and add it to both sides.

Add '25' to each side of the equation.

-10x + 25 + x2 = -13 + 25

Reorder the terms:

25 + -10x + x2 = -13 + 25

Combine like terms: -13 + 25 = 12

25 + -10x + x2 = 12

Factor a perfect square on the left side:

(x + -5)(x + -5) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting  

(x + -5) equal to 3.464101615 and -3.464101615.