18x^2+24x-8=0

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Solution for 18x^2+24x-8=0 equation:


Simplifying
18x2 + 24x + -8 = 0

Reorder the terms:
-8 + 24x + 18x2 = 0

Solving
-8 + 24x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 12x + 9x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + 12x + 9x2 = 0 Solving -4 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.333333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.4444444444 1.333333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.333333333x + x2 = 0.4444444444 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.4444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.4444444444 + 0.4444444442 Combine like terms: 0.4444444444 + 0.4444444442 = 0.8888888886 0.4444444442 + 1.333333333x + x2 = 0.8888888886 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.8888888886 Calculate the square root of the right side: 0.942809041 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.942809041 and -0.942809041.

Subproblem 1

x + 0.6666666665 = 0.942809041 Simplifying x + 0.6666666665 = 0.942809041 Reorder the terms: 0.6666666665 + x = 0.942809041 Solving 0.6666666665 + x = 0.942809041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.942809041 + -0.6666666665 x = 0.942809041 + -0.6666666665 Combine like terms: 0.942809041 + -0.6666666665 = 0.2761423745 x = 0.2761423745 Simplifying x = 0.2761423745

Subproblem 2

x + 0.6666666665 = -0.942809041 Simplifying x + 0.6666666665 = -0.942809041 Reorder the terms: 0.6666666665 + x = -0.942809041 Solving 0.6666666665 + x = -0.942809041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.942809041 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.942809041 + -0.6666666665 x = -0.942809041 + -0.6666666665 Combine like terms: -0.942809041 + -0.6666666665 = -1.6094757075 x = -1.6094757075 Simplifying x = -1.6094757075

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2761423745, -1.6094757075}

Solution

x = {0.2761423745, -1.6094757075}

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