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Simplifying 4(m2 + -6m) = 9 Reorder the terms: 4(-6m + m2) = 9 (-6m * 4 + m2 * 4) = 9 (-24m + 4m2) = 9 Solving -24m + 4m2 = 9 Solving for variable 'm'. Reorder the terms: -9 + -24m + 4m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -24m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -6m + m2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -6m + 2.25 + m2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -6m + m2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -6m + m2 = 0 + 2.25 -6m + m2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -6m + m2 = 2.25 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 = 2.25 + 9 Reorder the terms: 9 + -6m + m2 = 2.25 + 9 Combine like terms: 2.25 + 9 = 11.25 9 + -6m + m2 = 11.25 Factor a perfect square on the left side: (m + -3)(m + -3) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (m + -3) equal to 3.354101966 and -3.354101966.Subproblem 1
m + -3 = 3.354101966 Simplifying m + -3 = 3.354101966 Reorder the terms: -3 + m = 3.354101966 Solving -3 + m = 3.354101966 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 = 3.354101966 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.354101966 + 3 m = 3.354101966 + 3 Combine like terms: 3.354101966 + 3 = 6.354101966 m = 6.354101966 Simplifying m = 6.354101966Subproblem 2
m + -3 = -3.354101966 Simplifying m + -3 = -3.354101966 Reorder the terms: -3 + m = -3.354101966 Solving -3 + m = -3.354101966 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 = -3.354101966 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.354101966 + 3 m = -3.354101966 + 3 Combine like terms: -3.354101966 + 3 = -0.354101966 m = -0.354101966 Simplifying m = -0.354101966Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.354101966, -0.354101966}
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