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.
