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Simplifying 90 + -40m + 4m2 = 0 Solving 90 + -40m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -20m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -20m + 2m2)' equal to zero and attempt to solve: Simplifying 45 + -20m + 2m2 = 0 Solving 45 + -20m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + -10m + m2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -10m + -22.5 + m2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -10m + m2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -10m + m2 = 0 + -22.5 -10m + m2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -10m + m2 = -22.5 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = -22.5 + 25 Reorder the terms: 25 + -10m + m2 = -22.5 + 25 Combine like terms: -22.5 + 25 = 2.5 25 + -10m + m2 = 2.5 Factor a perfect square on the left side: (m + -5)(m + -5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (m + -5) equal to 1.58113883 and -1.58113883.Subproblem 1
m + -5 = 1.58113883 Simplifying m + -5 = 1.58113883 Reorder the terms: -5 + m = 1.58113883 Solving -5 + m = 1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 1.58113883 + 5 Combine like terms: -5 + 5 = 0 0 + m = 1.58113883 + 5 m = 1.58113883 + 5 Combine like terms: 1.58113883 + 5 = 6.58113883 m = 6.58113883 Simplifying m = 6.58113883Subproblem 2
m + -5 = -1.58113883 Simplifying m + -5 = -1.58113883 Reorder the terms: -5 + m = -1.58113883 Solving -5 + m = -1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -1.58113883 + 5 Combine like terms: -5 + 5 = 0 0 + m = -1.58113883 + 5 m = -1.58113883 + 5 Combine like terms: -1.58113883 + 5 = 3.41886117 m = 3.41886117 Simplifying m = 3.41886117Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.58113883, 3.41886117}Solution
m = {6.58113883, 3.41886117}
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