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Simplifying -1(15m2 + 6m3) + -1(-5m) = 0 (15m2 * -1 + 6m3 * -1) + -1(-5m) = 0 (-15m2 + -6m3) + -1(-5m) = 0 Remove parenthesis around (-5m) -15m2 + -6m3 + -1 * -5m = 0 Multiply -1 * -5 -15m2 + -6m3 + 5m = 0 Reorder the terms: 5m + -15m2 + -6m3 = 0 Solving 5m + -15m2 + -6m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(5 + -15m + -6m2) = 0Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(5 + -15m + -6m2)' equal to zero and attempt to solve: Simplifying 5 + -15m + -6m2 = 0 Solving 5 + -15m + -6m2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + 2.5m + m2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 2.5m + 0.8333333333 + m2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 2.5m + m2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 2.5m + m2 = 0 + 0.8333333333 2.5m + m2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 2.5m + m2 = 0.8333333333 The m term is 2.5m. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5m + 1.5625 + m2 = 0.8333333333 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 0.8333333333 + 1.5625 Combine like terms: 0.8333333333 + 1.5625 = 2.3958333333 1.5625 + 2.5m + m2 = 2.3958333333 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 2.3958333333 Calculate the square root of the right side: 1.547847968 Break this problem into two subproblems by setting (m + 1.25) equal to 1.547847968 and -1.547847968.Subproblem 1
m + 1.25 = 1.547847968 Simplifying m + 1.25 = 1.547847968 Reorder the terms: 1.25 + m = 1.547847968 Solving 1.25 + m = 1.547847968 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = 1.547847968 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 1.547847968 + -1.25 m = 1.547847968 + -1.25 Combine like terms: 1.547847968 + -1.25 = 0.297847968 m = 0.297847968 Simplifying m = 0.297847968Subproblem 2
m + 1.25 = -1.547847968 Simplifying m + 1.25 = -1.547847968 Reorder the terms: 1.25 + m = -1.547847968 Solving 1.25 + m = -1.547847968 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = -1.547847968 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -1.547847968 + -1.25 m = -1.547847968 + -1.25 Combine like terms: -1.547847968 + -1.25 = -2.797847968 m = -2.797847968 Simplifying m = -2.797847968Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.297847968, -2.797847968}Solution
m = {0, 0.297847968, -2.797847968}
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