6x^2-4x-140=0

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Solution for 6x^2-4x-140=0 equation:


Simplifying
6x2 + -4x + -140 = 0

Reorder the terms:
-140 + -4x + 6x2 = 0

Solving
-140 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + -2x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-70 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -70 + -2x + 3x2 = 0 Solving -70 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -23.33333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + -0.6666666667x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + -0.6666666667x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + -0.6666666667x + x2 = 0 + 23.33333333 -0.6666666667x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 -0.6666666667x + x2 = 23.33333333 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 = 23.33333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 23.33333333 + 0.1111111112 Combine like terms: 23.33333333 + 0.1111111112 = 23.4444444412 0.1111111112 + -0.6666666667x + x2 = 23.4444444412 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 23.4444444412 Calculate the square root of the right side: 4.841946348 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 4.841946348 and -4.841946348.

Subproblem 1

x + -0.3333333334 = 4.841946348 Simplifying x + -0.3333333334 = 4.841946348 Reorder the terms: -0.3333333334 + x = 4.841946348 Solving -0.3333333334 + x = 4.841946348 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 = 4.841946348 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 4.841946348 + 0.3333333334 x = 4.841946348 + 0.3333333334 Combine like terms: 4.841946348 + 0.3333333334 = 5.1752796814 x = 5.1752796814 Simplifying x = 5.1752796814

Subproblem 2

x + -0.3333333334 = -4.841946348 Simplifying x + -0.3333333334 = -4.841946348 Reorder the terms: -0.3333333334 + x = -4.841946348 Solving -0.3333333334 + x = -4.841946348 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 = -4.841946348 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -4.841946348 + 0.3333333334 x = -4.841946348 + 0.3333333334 Combine like terms: -4.841946348 + 0.3333333334 = -4.5086130146 x = -4.5086130146 Simplifying x = -4.5086130146

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.1752796814, -4.5086130146}

Solution

x = {5.1752796814, -4.5086130146}

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