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Simplifying -4m2 + -4m + 5 = 0 Reorder the terms: 5 + -4m + -4m2 = 0 Solving 5 + -4m + -4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + m + m2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + m + 1.25 + m2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + m + m2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m + m2 = 0 + 1.25 m + m2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 m + m2 = 1.25 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 1.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 1.25 + m2 = 1.5 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (m + 0.5) equal to 1.224744871 and -1.224744871.Subproblem 1
m + 0.5 = 1.224744871 Simplifying m + 0.5 = 1.224744871 Reorder the terms: 0.5 + m = 1.224744871 Solving 0.5 + m = 1.224744871 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.224744871 + -0.5 m = 1.224744871 + -0.5 Combine like terms: 1.224744871 + -0.5 = 0.724744871 m = 0.724744871 Simplifying m = 0.724744871Subproblem 2
m + 0.5 = -1.224744871 Simplifying m + 0.5 = -1.224744871 Reorder the terms: 0.5 + m = -1.224744871 Solving 0.5 + m = -1.224744871 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.224744871 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.224744871 + -0.5 m = -1.224744871 + -0.5 Combine like terms: -1.224744871 + -0.5 = -1.724744871 m = -1.724744871 Simplifying m = -1.724744871Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.724744871, -1.724744871}
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