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Simplifying 4m2 + -24m + 36 = 10 Reorder the terms: 36 + -24m + 4m2 = 10 Solving 36 + -24m + 4m2 = 10 Solving for variable 'm'. Reorder the terms: 36 + -10 + -24m + 4m2 = 10 + -10 Combine like terms: 36 + -10 = 26 26 + -24m + 4m2 = 10 + -10 Combine like terms: 10 + -10 = 0 26 + -24m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -12m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -12m + 2m2)' equal to zero and attempt to solve: Simplifying 13 + -12m + 2m2 = 0 Solving 13 + -12m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -6m + m2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -6m + -6.5 + m2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -6m + m2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -6m + m2 = 0 + -6.5 -6m + m2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -6m + m2 = -6.5 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 = -6.5 + 9 Reorder the terms: 9 + -6m + m2 = -6.5 + 9 Combine like terms: -6.5 + 9 = 2.5 9 + -6m + m2 = 2.5 Factor a perfect square on the left side: (m + -3)(m + -3) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (m + -3) equal to 1.58113883 and -1.58113883.Subproblem 1
m + -3 = 1.58113883 Simplifying m + -3 = 1.58113883 Reorder the terms: -3 + m = 1.58113883 Solving -3 + m = 1.58113883 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 = 1.58113883 + 3 Combine like terms: -3 + 3 = 0 0 + m = 1.58113883 + 3 m = 1.58113883 + 3 Combine like terms: 1.58113883 + 3 = 4.58113883 m = 4.58113883 Simplifying m = 4.58113883Subproblem 2
m + -3 = -1.58113883 Simplifying m + -3 = -1.58113883 Reorder the terms: -3 + m = -1.58113883 Solving -3 + m = -1.58113883 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 = -1.58113883 + 3 Combine like terms: -3 + 3 = 0 0 + m = -1.58113883 + 3 m = -1.58113883 + 3 Combine like terms: -1.58113883 + 3 = 1.41886117 m = 1.41886117 Simplifying m = 1.41886117Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.58113883, 1.41886117}Solution
m = {4.58113883, 1.41886117}
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