12x+18x^2-42=0

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Solution for 12x+18x^2-42=0 equation:


Simplifying
12x + 18x2 + -42 = 0

Reorder the terms:
-42 + 12x + 18x2 = 0

Solving
-42 + 12x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + 2x + 3x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-7 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying -7 + 2x + 3x2 = 0 Solving -7 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 0.6666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 0.6666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 2.333333333 0.6666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 0.6666666667x + x2 = 2.333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 2.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 2.333333333 + 0.1111111112 Combine like terms: 2.333333333 + 0.1111111112 = 2.4444444442 0.1111111112 + 0.6666666667x + x2 = 2.4444444442 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.4444444442 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.56347192 and -1.56347192.

Subproblem 1

x + 0.3333333334 = 1.56347192 Simplifying x + 0.3333333334 = 1.56347192 Reorder the terms: 0.3333333334 + x = 1.56347192 Solving 0.3333333334 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.56347192 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.56347192 + -0.3333333334 x = 1.56347192 + -0.3333333334 Combine like terms: 1.56347192 + -0.3333333334 = 1.2301385866 x = 1.2301385866 Simplifying x = 1.2301385866

Subproblem 2

x + 0.3333333334 = -1.56347192 Simplifying x + 0.3333333334 = -1.56347192 Reorder the terms: 0.3333333334 + x = -1.56347192 Solving 0.3333333334 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.56347192 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.56347192 + -0.3333333334 x = -1.56347192 + -0.3333333334 Combine like terms: -1.56347192 + -0.3333333334 = -1.8968052534 x = -1.8968052534 Simplifying x = -1.8968052534

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2301385866, -1.8968052534}

Solution

x = {1.2301385866, -1.8968052534}

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