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Simplifying -2m2 + -8m + 40 = 0 Reorder the terms: 40 + -8m + -2m2 = 0 Solving 40 + -8m + -2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -4m + -1m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -4m + -1m2)' equal to zero and attempt to solve: Simplifying 20 + -4m + -1m2 = 0 Solving 20 + -4m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 4m + m2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 4m + 20 + m2 = 0 + 20 Reorder the terms: -20 + 20 + 4m + m2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4m + m2 = 0 + 20 4m + m2 = 0 + 20 Combine like terms: 0 + 20 = 20 4m + m2 = 20 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = 20 + 4 Reorder the terms: 4 + 4m + m2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4m + m2 = 24 Factor a perfect square on the left side: (m + 2)(m + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (m + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
m + 2 = 4.898979486 Simplifying m + 2 = 4.898979486 Reorder the terms: 2 + m = 4.898979486 Solving 2 + m = 4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + m = 4.898979486 + -2 m = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 m = 2.898979486 Simplifying m = 2.898979486Subproblem 2
m + 2 = -4.898979486 Simplifying m + 2 = -4.898979486 Reorder the terms: 2 + m = -4.898979486 Solving 2 + m = -4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + m = -4.898979486 + -2 m = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 m = -6.898979486 Simplifying m = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.898979486, -6.898979486}Solution
m = {2.898979486, -6.898979486}
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