Answer:
Simplifying
x2 + -10x + 23 = 0
Reorder the terms:
23 + -10x + x2 = 0
Solving
23 + -10x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '-23' to each side of the equation.
23 + -10x + -23 + x2 = 0 + -23
Reorder the terms:
23 + -23 + -10x + x2 = 0 + -23
Combine like terms: 23 + -23 = 0
0 + -10x + x2 = 0 + -23
-10x + x2 = 0 + -23
Combine like terms: 0 + -23 = -23
-10x + x2 = -23
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 = -23 + 25
Reorder the terms:
25 + -10x + x2 = -23 + 25
Combine like terms: -23 + 25 = 2
25 + -10x + x2 = 2
Factor a perfect square on the left side:
(x + -5)(x + -5) = 2
Calculate the square root of the right side: 1.414213562
Break this problem into two subproblems by setting
(x + -5) equal to 1.414213562 and -1.414213562.
Subproblem 1
x + -5 = 1.414213562
Simplifying
x + -5 = 1.414213562
Reorder the terms:
-5 + x = 1.414213562
Solving
-5 + x = 1.414213562
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + x = 1.414213562 + 5
Combine like terms: -5 + 5 = 0
0 + x = 1.414213562 + 5
x = 1.414213562 + 5
Combine like terms: 1.414213562 + 5 = 6.414213562
x = 6.414213562
Simplifying
x = 6.414213562
Subproblem 2
x + -5 = -1.414213562
Simplifying
x + -5 = -1.414213562
Reorder the terms:
-5 + x = -1.414213562
Solving
-5 + x = -1.414213562
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + x = -1.414213562 + 5
Combine like terms: -5 + 5 = 0
0 + x = -1.414213562 + 5
x = -1.414213562 + 5
Combine like terms: -1.414213562 + 5 = 3.585786438
x = 3.585786438
Simplifying
x = 3.585786438
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.414213562, 3.585786438}
Step-by-step explanation:
