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Simplifying 2m(m + -7) + -5(6m + -6) = 0 Reorder the terms: 2m(-7 + m) + -5(6m + -6) = 0 (-7 * 2m + m * 2m) + -5(6m + -6) = 0 (-14m + 2m2) + -5(6m + -6) = 0 Reorder the terms: -14m + 2m2 + -5(-6 + 6m) = 0 -14m + 2m2 + (-6 * -5 + 6m * -5) = 0 -14m + 2m2 + (30 + -30m) = 0 Reorder the terms: 30 + -14m + -30m + 2m2 = 0 Combine like terms: -14m + -30m = -44m 30 + -44m + 2m2 = 0 Solving 30 + -44m + 2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -22m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -22m + m2)' equal to zero and attempt to solve: Simplifying 15 + -22m + m2 = 0 Solving 15 + -22m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -22m + -15 + m2 = 0 + -15 Reorder the terms: 15 + -15 + -22m + m2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -22m + m2 = 0 + -15 -22m + m2 = 0 + -15 Combine like terms: 0 + -15 = -15 -22m + m2 = -15 The m term is -22m. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22m + 121 + m2 = -15 + 121 Reorder the terms: 121 + -22m + m2 = -15 + 121 Combine like terms: -15 + 121 = 106 121 + -22m + m2 = 106 Factor a perfect square on the left side: (m + -11)(m + -11) = 106 Calculate the square root of the right side: 10.295630141 Break this problem into two subproblems by setting (m + -11) equal to 10.295630141 and -10.295630141.Subproblem 1
m + -11 = 10.295630141 Simplifying m + -11 = 10.295630141 Reorder the terms: -11 + m = 10.295630141 Solving -11 + m = 10.295630141 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + m = 10.295630141 + 11 Combine like terms: -11 + 11 = 0 0 + m = 10.295630141 + 11 m = 10.295630141 + 11 Combine like terms: 10.295630141 + 11 = 21.295630141 m = 21.295630141 Simplifying m = 21.295630141Subproblem 2
m + -11 = -10.295630141 Simplifying m + -11 = -10.295630141 Reorder the terms: -11 + m = -10.295630141 Solving -11 + m = -10.295630141 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + m = -10.295630141 + 11 Combine like terms: -11 + 11 = 0 0 + m = -10.295630141 + 11 m = -10.295630141 + 11 Combine like terms: -10.295630141 + 11 = 0.704369859 m = 0.704369859 Simplifying m = 0.704369859Solution
The solution to the problem is based on the solutions from the subproblems. m = {21.295630141, 0.704369859}Solution
m = {21.295630141, 0.704369859}
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