-18x+x^2=-40

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Solution for -18x+x^2=-40 equation:


Simplifying
-18x + x2 = -40

Solving
-18x + x2 = -40

Solving for variable 'x'.

Reorder the terms:
40 + -18x + x2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -18x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + -18x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -18x + x2 = 0 + -40
-18x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-18x + x2 = -40

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -40 + 81

Reorder the terms:
81 + -18x + x2 = -40 + 81

Combine like terms: -40 + 81 = 41
81 + -18x + x2 = 41

Factor a perfect square on the left side:
(x + -9)(x + -9) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -9) equal to 6.403124237 and -6.403124237.

Subproblem 1

x + -9 = 6.403124237 Simplifying x + -9 = 6.403124237 Reorder the terms: -9 + x = 6.403124237 Solving -9 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6.403124237 + 9 x = 6.403124237 + 9 Combine like terms: 6.403124237 + 9 = 15.403124237 x = 15.403124237 Simplifying x = 15.403124237

Subproblem 2

x + -9 = -6.403124237 Simplifying x + -9 = -6.403124237 Reorder the terms: -9 + x = -6.403124237 Solving -9 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6.403124237 + 9 x = -6.403124237 + 9 Combine like terms: -6.403124237 + 9 = 2.596875763 x = 2.596875763 Simplifying x = 2.596875763

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.403124237, 2.596875763}

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