5x^2-18x=-12

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Solution for 5x^2-18x=-12 equation:


Simplifying
5x2 + -18x = -12

Reorder the terms:
-18x + 5x2 = -12

Solving
-18x + 5x2 = -12

Solving for variable 'x'.

Reorder the terms:
12 + -18x + 5x2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -18x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.4 + -3.6x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -3.6x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -3.6x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -3.6x + x2 = 0 + -2.4
-3.6x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-3.6x + x2 = -2.4

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = -2.4 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = -2.4 + 3.24

Combine like terms: -2.4 + 3.24 = 0.84
3.24 + -3.6x + x2 = 0.84

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(x + -1.8) equal to 0.916515139 and -0.916515139.

Subproblem 1

x + -1.8 = 0.916515139 Simplifying x + -1.8 = 0.916515139 Reorder the terms: -1.8 + x = 0.916515139 Solving -1.8 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.916515139 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.916515139 + 1.8 x = 0.916515139 + 1.8 Combine like terms: 0.916515139 + 1.8 = 2.716515139 x = 2.716515139 Simplifying x = 2.716515139

Subproblem 2

x + -1.8 = -0.916515139 Simplifying x + -1.8 = -0.916515139 Reorder the terms: -1.8 + x = -0.916515139 Solving -1.8 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.916515139 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.916515139 + 1.8 x = -0.916515139 + 1.8 Combine like terms: -0.916515139 + 1.8 = 0.883484861 x = 0.883484861 Simplifying x = 0.883484861

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.716515139, 0.883484861}

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