18x^2-6x=15

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Solution for 18x^2-6x=15 equation:


Simplifying
18x2 + -6x = 15

Reorder the terms:
-6x + 18x2 = 15

Solving
-6x + 18x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -6x + 18x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -6x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -2x + 6x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + -2x + 6x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + 6x2 = 0 Solving -5 + -2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.3333333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.3333333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.3333333333x + x2 = 0 + 0.8333333333 -0.3333333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.3333333333x + x2 = 0.8333333333 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.8333333333 + 0.02777777779 Combine like terms: 0.8333333333 + 0.02777777779 = 0.86111111109 0.02777777779 + -0.3333333333x + x2 = 0.86111111109 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.86111111109 Calculate the square root of the right side: 0.927960727 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.927960727 and -0.927960727.

Subproblem 1

x + -0.1666666667 = 0.927960727 Simplifying x + -0.1666666667 = 0.927960727 Reorder the terms: -0.1666666667 + x = 0.927960727 Solving -0.1666666667 + x = 0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.927960727 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.927960727 + 0.1666666667 x = 0.927960727 + 0.1666666667 Combine like terms: 0.927960727 + 0.1666666667 = 1.0946273937 x = 1.0946273937 Simplifying x = 1.0946273937

Subproblem 2

x + -0.1666666667 = -0.927960727 Simplifying x + -0.1666666667 = -0.927960727 Reorder the terms: -0.1666666667 + x = -0.927960727 Solving -0.1666666667 + x = -0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.927960727 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.927960727 + 0.1666666667 x = -0.927960727 + 0.1666666667 Combine like terms: -0.927960727 + 0.1666666667 = -0.7612940603 x = -0.7612940603 Simplifying x = -0.7612940603

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0946273937, -0.7612940603}

Solution

x = {1.0946273937, -0.7612940603}

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