6m^2-6m-4=

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Solution for 6m^2-6m-4= equation:


Simplifying
6m2 + -6m + -4 = 0

Reorder the terms:
-4 + -6m + 6m2 = 0

Solving
-4 + -6m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -3m + 3m2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -3m + 3m2)' equal to zero and attempt to solve: Simplifying -2 + -3m + 3m2 = 0 Solving -2 + -3m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -1m + m2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -1m + 0.6666666667 + m2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -1m + m2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -1m + m2 = 0 + 0.6666666667 -1m + m2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -1m + m2 = 0.6666666667 The m term is -1m. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1m + 0.25 + m2 = 0.6666666667 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 0.25 + -1m + m2 = 0.9166666667 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (m + -0.5) equal to 0.957427108 and -0.957427108.

Subproblem 1

m + -0.5 = 0.957427108 Simplifying m + -0.5 = 0.957427108 Reorder the terms: -0.5 + m = 0.957427108 Solving -0.5 + m = 0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = 0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 0.957427108 + 0.5 m = 0.957427108 + 0.5 Combine like terms: 0.957427108 + 0.5 = 1.457427108 m = 1.457427108 Simplifying m = 1.457427108

Subproblem 2

m + -0.5 = -0.957427108 Simplifying m + -0.5 = -0.957427108 Reorder the terms: -0.5 + m = -0.957427108 Solving -0.5 + m = -0.957427108 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + m = -0.957427108 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -0.957427108 + 0.5 m = -0.957427108 + 0.5 Combine like terms: -0.957427108 + 0.5 = -0.457427108 m = -0.457427108 Simplifying m = -0.457427108

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.457427108, -0.457427108}

Solution

m = {1.457427108, -0.457427108}

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