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Simplifying 2 + 5(m + -8) * m = -2 Reorder the terms: 2 + 5(-8 + m) * m = -2 Reorder the terms for easier multiplication: 2 + 5m(-8 + m) = -2 2 + (-8 * 5m + m * 5m) = -2 2 + (-40m + 5m2) = -2 Solving 2 + -40m + 5m2 = -2 Solving for variable 'm'. Reorder the terms: 2 + 2 + -40m + 5m2 = -2 + 2 Combine like terms: 2 + 2 = 4 4 + -40m + 5m2 = -2 + 2 Combine like terms: -2 + 2 = 0 4 + -40m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -8m + m2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -8m + -0.8 + m2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -8m + m2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -8m + m2 = 0 + -0.8 -8m + m2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -8m + m2 = -0.8 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = -0.8 + 16 Reorder the terms: 16 + -8m + m2 = -0.8 + 16 Combine like terms: -0.8 + 16 = 15.2 16 + -8m + m2 = 15.2 Factor a perfect square on the left side: (m + -4)(m + -4) = 15.2 Calculate the square root of the right side: 3.898717738 Break this problem into two subproblems by setting (m + -4) equal to 3.898717738 and -3.898717738.Subproblem 1
m + -4 = 3.898717738 Simplifying m + -4 = 3.898717738 Reorder the terms: -4 + m = 3.898717738 Solving -4 + m = 3.898717738 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.898717738 + 4 m = 3.898717738 + 4 Combine like terms: 3.898717738 + 4 = 7.898717738 m = 7.898717738 Simplifying m = 7.898717738Subproblem 2
m + -4 = -3.898717738 Simplifying m + -4 = -3.898717738 Reorder the terms: -4 + m = -3.898717738 Solving -4 + m = -3.898717738 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.898717738 + 4 m = -3.898717738 + 4 Combine like terms: -3.898717738 + 4 = 0.101282262 m = 0.101282262 Simplifying m = 0.101282262Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.898717738, 0.101282262}
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