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Simplifying 5m(4m + -1) = 12 Reorder the terms: 5m(-1 + 4m) = 12 (-1 * 5m + 4m * 5m) = 12 (-5m + 20m2) = 12 Solving -5m + 20m2 = 12 Solving for variable 'm'. Reorder the terms: -12 + -5m + 20m2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -5m + 20m2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.6 + -0.25m + m2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.25m + 0.6 + m2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.25m + m2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.25m + m2 = 0.0 + 0.6 -0.25m + m2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -0.25m + m2 = 0.6 The m term is -0.25m. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25m + 0.015625 + m2 = 0.6 + 0.015625 Reorder the terms: 0.015625 + -0.25m + m2 = 0.6 + 0.015625 Combine like terms: 0.6 + 0.015625 = 0.615625 0.015625 + -0.25m + m2 = 0.615625 Factor a perfect square on the left side: (m + -0.125)(m + -0.125) = 0.615625 Calculate the square root of the right side: 0.784617741 Break this problem into two subproblems by setting (m + -0.125) equal to 0.784617741 and -0.784617741.Subproblem 1
m + -0.125 = 0.784617741 Simplifying m + -0.125 = 0.784617741 Reorder the terms: -0.125 + m = 0.784617741 Solving -0.125 + m = 0.784617741 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + m = 0.784617741 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = 0.784617741 + 0.125 m = 0.784617741 + 0.125 Combine like terms: 0.784617741 + 0.125 = 0.909617741 m = 0.909617741 Simplifying m = 0.909617741Subproblem 2
m + -0.125 = -0.784617741 Simplifying m + -0.125 = -0.784617741 Reorder the terms: -0.125 + m = -0.784617741 Solving -0.125 + m = -0.784617741 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + m = -0.784617741 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + m = -0.784617741 + 0.125 m = -0.784617741 + 0.125 Combine like terms: -0.784617741 + 0.125 = -0.659617741 m = -0.659617741 Simplifying m = -0.659617741Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.909617741, -0.659617741}
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