-2m^2+12m+74=0

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Solution for -2m^2+12m+74=0 equation:


Simplifying
-2m2 + 12m + 74 = 0

Reorder the terms:
74 + 12m + -2m2 = 0

Solving
74 + 12m + -2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(37 + 6m + -1m2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(37 + 6m + -1m2)' equal to zero and attempt to solve: Simplifying 37 + 6m + -1m2 = 0 Solving 37 + 6m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -6m + m2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -6m + 37 + m2 = 0 + 37 Reorder the terms: -37 + 37 + -6m + m2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -6m + m2 = 0 + 37 -6m + m2 = 0 + 37 Combine like terms: 0 + 37 = 37 -6m + m2 = 37 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = 37 + 9 Reorder the terms: 9 + -6m + m2 = 37 + 9 Combine like terms: 37 + 9 = 46 9 + -6m + m2 = 46 Factor a perfect square on the left side: (m + -3)(m + -3) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (m + -3) equal to 6.782329983 and -6.782329983.

Subproblem 1

m + -3 = 6.782329983 Simplifying m + -3 = 6.782329983 Reorder the terms: -3 + m = 6.782329983 Solving -3 + m = 6.782329983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + m = 6.782329983 + 3 m = 6.782329983 + 3 Combine like terms: 6.782329983 + 3 = 9.782329983 m = 9.782329983 Simplifying m = 9.782329983

Subproblem 2

m + -3 = -6.782329983 Simplifying m + -3 = -6.782329983 Reorder the terms: -3 + m = -6.782329983 Solving -3 + m = -6.782329983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + m = -6.782329983 + 3 m = -6.782329983 + 3 Combine like terms: -6.782329983 + 3 = -3.782329983 m = -3.782329983 Simplifying m = -3.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. m = {9.782329983, -3.782329983}

Solution

m = {9.782329983, -3.782329983}

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