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Simplifying 4m2 + 5m = 7 Reorder the terms: 5m + 4m2 = 7 Solving 5m + 4m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + 5m + 4m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 5m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 1.25m + m2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 1.25m + 1.75 + m2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 1.25m + m2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 1.25m + m2 = 0 + 1.75 1.25m + m2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 1.25m + m2 = 1.75 The m term is 1.25m. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25m + 0.390625 + m2 = 1.75 + 0.390625 Reorder the terms: 0.390625 + 1.25m + m2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + 1.25m + m2 = 2.140625 Factor a perfect square on the left side: (m + 0.625)(m + 0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (m + 0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
m + 0.625 = 1.463087489 Simplifying m + 0.625 = 1.463087489 Reorder the terms: 0.625 + m = 1.463087489 Solving 0.625 + m = 1.463087489 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + m = 1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + m = 1.463087489 + -0.625 m = 1.463087489 + -0.625 Combine like terms: 1.463087489 + -0.625 = 0.838087489 m = 0.838087489 Simplifying m = 0.838087489Subproblem 2
m + 0.625 = -1.463087489 Simplifying m + 0.625 = -1.463087489 Reorder the terms: 0.625 + m = -1.463087489 Solving 0.625 + m = -1.463087489 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + m = -1.463087489 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + m = -1.463087489 + -0.625 m = -1.463087489 + -0.625 Combine like terms: -1.463087489 + -0.625 = -2.088087489 m = -2.088087489 Simplifying m = -2.088087489Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.838087489, -2.088087489}
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