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Simplifying -5m2 + 2m + 4 = 0 Reorder the terms: 4 + 2m + -5m2 = 0 Solving 4 + 2m + -5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -0.4m + m2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.4m + 0.8 + m2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.4m + m2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.4m + m2 = 0 + 0.8 -0.4m + m2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.4m + m2 = 0.8 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 0.8 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + -0.4m + m2 = 0.84 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (m + -0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
m + -0.2 = 0.916515139 Simplifying m + -0.2 = 0.916515139 Reorder the terms: -0.2 + m = 0.916515139 Solving -0.2 + m = 0.916515139 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 0.916515139 + 0.2 m = 0.916515139 + 0.2 Combine like terms: 0.916515139 + 0.2 = 1.116515139 m = 1.116515139 Simplifying m = 1.116515139Subproblem 2
m + -0.2 = -0.916515139 Simplifying m + -0.2 = -0.916515139 Reorder the terms: -0.2 + m = -0.916515139 Solving -0.2 + m = -0.916515139 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -0.916515139 + 0.2 m = -0.916515139 + 0.2 Combine like terms: -0.916515139 + 0.2 = -0.716515139 m = -0.716515139 Simplifying m = -0.716515139Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.116515139, -0.716515139}
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