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Simplifying 2m2 + 4m + -68 = 0 Reorder the terms: -68 + 4m + 2m2 = 0 Solving -68 + 4m + 2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-34 + 2m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-34 + 2m + m2)' equal to zero and attempt to solve: Simplifying -34 + 2m + m2 = 0 Solving -34 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 2m + 34 + m2 = 0 + 34 Reorder the terms: -34 + 34 + 2m + m2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 2m + m2 = 0 + 34 2m + m2 = 0 + 34 Combine like terms: 0 + 34 = 34 2m + m2 = 34 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 34 + 1 Reorder the terms: 1 + 2m + m2 = 34 + 1 Combine like terms: 34 + 1 = 35 1 + 2m + m2 = 35 Factor a perfect square on the left side: (m + 1)(m + 1) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (m + 1) equal to 5.916079783 and -5.916079783.Subproblem 1
m + 1 = 5.916079783 Simplifying m + 1 = 5.916079783 Reorder the terms: 1 + m = 5.916079783 Solving 1 + m = 5.916079783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + m = 5.916079783 + -1 m = 5.916079783 + -1 Combine like terms: 5.916079783 + -1 = 4.916079783 m = 4.916079783 Simplifying m = 4.916079783Subproblem 2
m + 1 = -5.916079783 Simplifying m + 1 = -5.916079783 Reorder the terms: 1 + m = -5.916079783 Solving 1 + m = -5.916079783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + m = -5.916079783 + -1 m = -5.916079783 + -1 Combine like terms: -5.916079783 + -1 = -6.916079783 m = -6.916079783 Simplifying m = -6.916079783Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.916079783, -6.916079783}Solution
m = {4.916079783, -6.916079783}
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