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Simplifying 4m + 2m(m + -3) = 6 Reorder the terms: 4m + 2m(-3 + m) = 6 4m + (-3 * 2m + m * 2m) = 6 4m + (-6m + 2m2) = 6 Combine like terms: 4m + -6m = -2m -2m + 2m2 = 6 Solving -2m + 2m2 = 6 Solving for variable 'm'. Reorder the terms: -6 + -2m + 2m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -2m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -1m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1m + m2)' equal to zero and attempt to solve: Simplifying -3 + -1m + m2 = 0 Solving -3 + -1m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -1m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1m + m2 = 0 + 3 -1m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1m + m2 = 3 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 = 3 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1m + m2 = 3.25 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + -0.5 = 1.802775638 Simplifying m + -0.5 = 1.802775638 Reorder the terms: -0.5 + m = 1.802775638 Solving -0.5 + m = 1.802775638 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 = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 1.802775638 + 0.5 m = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 m = 2.302775638 Simplifying m = 2.302775638Subproblem 2
m + -0.5 = -1.802775638 Simplifying m + -0.5 = -1.802775638 Reorder the terms: -0.5 + m = -1.802775638 Solving -0.5 + m = -1.802775638 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 = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -1.802775638 + 0.5 m = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 m = -1.302775638 Simplifying m = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.302775638, -1.302775638}Solution
m = {2.302775638, -1.302775638}
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