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Simplifying m2 = -7m + 4 Reorder the terms: m2 = 4 + -7m Solving m2 = 4 + -7m Solving for variable 'm'. Reorder the terms: -4 + 7m + m2 = 4 + -7m + -4 + 7m Reorder the terms: -4 + 7m + m2 = 4 + -4 + -7m + 7m Combine like terms: 4 + -4 = 0 -4 + 7m + m2 = 0 + -7m + 7m -4 + 7m + m2 = -7m + 7m Combine like terms: -7m + 7m = 0 -4 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 7m + 4 + m2 = 0 + 4 Reorder the terms: -4 + 4 + 7m + m2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7m + m2 = 0 + 4 7m + m2 = 0 + 4 Combine like terms: 0 + 4 = 4 7m + m2 = 4 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 4 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7m + m2 = 16.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (m + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
m + 3.5 = 4.031128874 Simplifying m + 3.5 = 4.031128874 Reorder the terms: 3.5 + m = 4.031128874 Solving 3.5 + m = 4.031128874 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 4.031128874 + -3.5 m = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 m = 0.531128874 Simplifying m = 0.531128874Subproblem 2
m + 3.5 = -4.031128874 Simplifying m + 3.5 = -4.031128874 Reorder the terms: 3.5 + m = -4.031128874 Solving 3.5 + m = -4.031128874 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -4.031128874 + -3.5 m = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 m = -7.531128874 Simplifying m = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.531128874, -7.531128874}
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