x^2-10x=-18

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Solution for x^2-10x=-18 equation:


Simplifying
x2 + -10x = -18

Reorder the terms:
-10x + x2 = -18

Solving
-10x + x2 = -18

Solving for variable 'x'.

Reorder the terms:
18 + -10x + x2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -10x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10x + x2 = 0 + -18
-10x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10x + x2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10x + x2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10x + x2 = 7

Factor a perfect square on the left side:
(x + -5)(x + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -5) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -5 = 2.645751311 Simplifying x + -5 = 2.645751311 Reorder the terms: -5 + x = 2.645751311 Solving -5 + x = 2.645751311 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 = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.645751311 + 5 x = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 x = 7.645751311 Simplifying x = 7.645751311

Subproblem 2

x + -5 = -2.645751311 Simplifying x + -5 = -2.645751311 Reorder the terms: -5 + x = -2.645751311 Solving -5 + x = -2.645751311 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 = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.645751311 + 5 x = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 x = 2.354248689 Simplifying x = 2.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.645751311, 2.354248689}

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