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Simplifying 2m + m2 + 2.5m + -2.5 = 0 Reorder the terms: -2.5 + 2m + 2.5m + m2 = 0 Combine like terms: 2m + 2.5m = 4.5m -2.5 + 4.5m + m2 = 0 Solving -2.5 + 4.5m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 4.5m + 2.5 + m2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 4.5m + m2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 4.5m + m2 = 0 + 2.5 4.5m + m2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 4.5m + m2 = 2.5 The m term is 4.5m. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5m + 5.0625 + m2 = 2.5 + 5.0625 Reorder the terms: 5.0625 + 4.5m + m2 = 2.5 + 5.0625 Combine like terms: 2.5 + 5.0625 = 7.5625 5.0625 + 4.5m + m2 = 7.5625 Factor a perfect square on the left side: (m + 2.25)(m + 2.25) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (m + 2.25) equal to 2.75 and -2.75.Subproblem 1
m + 2.25 = 2.75 Simplifying m + 2.25 = 2.75 Reorder the terms: 2.25 + m = 2.75 Solving 2.25 + m = 2.75 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = 2.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = 2.75 + -2.25 m = 2.75 + -2.25 Combine like terms: 2.75 + -2.25 = 0.5 m = 0.5 Simplifying m = 0.5Subproblem 2
m + 2.25 = -2.75 Simplifying m + 2.25 = -2.75 Reorder the terms: 2.25 + m = -2.75 Solving 2.25 + m = -2.75 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + m = -2.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + m = -2.75 + -2.25 m = -2.75 + -2.25 Combine like terms: -2.75 + -2.25 = -5 m = -5 Simplifying m = -5Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.5, -5}
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