x^2-3x=18*13

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Solution for x^2-3x=18*13 equation:


Simplifying
x2 + -3x = 18 * 13

Reorder the terms:
-3x + x2 = 18 * 13

Multiply 18 * 13
-3x + x2 = 234

Solving
-3x + x2 = 234

Solving for variable 'x'.

Reorder the terms:
-234 + -3x + x2 = 234 + -234

Combine like terms: 234 + -234 = 0
-234 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '234' to each side of the equation.
-234 + -3x + 234 + x2 = 0 + 234

Reorder the terms:
-234 + 234 + -3x + x2 = 0 + 234

Combine like terms: -234 + 234 = 0
0 + -3x + x2 = 0 + 234
-3x + x2 = 0 + 234

Combine like terms: 0 + 234 = 234
-3x + x2 = 234

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 234 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 234 + 2.25

Combine like terms: 234 + 2.25 = 236.25
2.25 + -3x + x2 = 236.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 236.25

Calculate the square root of the right side: 15.370426149

Break this problem into two subproblems by setting 
(x + -1.5) equal to 15.370426149 and -15.370426149.

Subproblem 1

x + -1.5 = 15.370426149 Simplifying x + -1.5 = 15.370426149 Reorder the terms: -1.5 + x = 15.370426149 Solving -1.5 + x = 15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 15.370426149 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 15.370426149 + 1.5 x = 15.370426149 + 1.5 Combine like terms: 15.370426149 + 1.5 = 16.870426149 x = 16.870426149 Simplifying x = 16.870426149

Subproblem 2

x + -1.5 = -15.370426149 Simplifying x + -1.5 = -15.370426149 Reorder the terms: -1.5 + x = -15.370426149 Solving -1.5 + x = -15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -15.370426149 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -15.370426149 + 1.5 x = -15.370426149 + 1.5 Combine like terms: -15.370426149 + 1.5 = -13.870426149 x = -13.870426149 Simplifying x = -13.870426149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.870426149, -13.870426149}

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