-12x^2-36x+2=0

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Solution for -12x^2-36x+2=0 equation:


Simplifying
-12x2 + -36x + 2 = 0

Reorder the terms:
2 + -36x + -12x2 = 0

Solving
2 + -36x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -18x + -6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + -18x + -6x2)' equal to zero and attempt to solve: Simplifying 1 + -18x + -6x2 = 0 Solving 1 + -18x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + 3x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 3x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 3x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + 0.1666666667 3x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 3x + x2 = 0.1666666667 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 = 0.1666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.1666666667 + 2.25 Combine like terms: 0.1666666667 + 2.25 = 2.4166666667 2.25 + 3x + x2 = 2.4166666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.4166666667 Calculate the square root of the right side: 1.554563176 Break this problem into two subproblems by setting (x + 1.5) equal to 1.554563176 and -1.554563176.

Subproblem 1

x + 1.5 = 1.554563176 Simplifying x + 1.5 = 1.554563176 Reorder the terms: 1.5 + x = 1.554563176 Solving 1.5 + x = 1.554563176 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 = 1.554563176 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.554563176 + -1.5 x = 1.554563176 + -1.5 Combine like terms: 1.554563176 + -1.5 = 0.054563176 x = 0.054563176 Simplifying x = 0.054563176

Subproblem 2

x + 1.5 = -1.554563176 Simplifying x + 1.5 = -1.554563176 Reorder the terms: 1.5 + x = -1.554563176 Solving 1.5 + x = -1.554563176 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 = -1.554563176 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.554563176 + -1.5 x = -1.554563176 + -1.5 Combine like terms: -1.554563176 + -1.5 = -3.054563176 x = -3.054563176 Simplifying x = -3.054563176

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.054563176, -3.054563176}

Solution

x = {0.054563176, -3.054563176}

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