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Simplifying 7m = -4m2 + 4 Reorder the terms: 7m = 4 + -4m2 Solving 7m = 4 + -4m2 Solving for variable 'm'. Reorder the terms: -4 + 7m + 4m2 = 4 + -4m2 + -4 + 4m2 Reorder the terms: -4 + 7m + 4m2 = 4 + -4 + -4m2 + 4m2 Combine like terms: 4 + -4 = 0 -4 + 7m + 4m2 = 0 + -4m2 + 4m2 -4 + 7m + 4m2 = -4m2 + 4m2 Combine like terms: -4m2 + 4m2 = 0 -4 + 7m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 1.75m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.75m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 1.75m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.75m + m2 = 0 + 1 1.75m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.75m + m2 = 1 The m term is 1.75m. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75m + 0.765625 + m2 = 1 + 0.765625 Reorder the terms: 0.765625 + 1.75m + m2 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + 1.75m + m2 = 1.765625 Factor a perfect square on the left side: (m + 0.875)(m + 0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (m + 0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
m + 0.875 = 1.328768227 Simplifying m + 0.875 = 1.328768227 Reorder the terms: 0.875 + m = 1.328768227 Solving 0.875 + m = 1.328768227 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + m = 1.328768227 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + m = 1.328768227 + -0.875 m = 1.328768227 + -0.875 Combine like terms: 1.328768227 + -0.875 = 0.453768227 m = 0.453768227 Simplifying m = 0.453768227Subproblem 2
m + 0.875 = -1.328768227 Simplifying m + 0.875 = -1.328768227 Reorder the terms: 0.875 + m = -1.328768227 Solving 0.875 + m = -1.328768227 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + m = -1.328768227 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + m = -1.328768227 + -0.875 m = -1.328768227 + -0.875 Combine like terms: -1.328768227 + -0.875 = -2.203768227 m = -2.203768227 Simplifying m = -2.203768227Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.453768227, -2.203768227}
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