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Simplifying 5m2 + 5m + -1 = 0 Reorder the terms: -1 + 5m + 5m2 = 0 Solving -1 + 5m + 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'. -0.2 + m + m2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + m + 0.2 + m2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + m + m2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m + m2 = 0 + 0.2 m + m2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 m + m2 = 0.2 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 = 0.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 1.25 + m2 = 0.45 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (m + 0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
m + 0.5 = 0.670820393 Simplifying m + 0.5 = 0.670820393 Reorder the terms: 0.5 + m = 0.670820393 Solving 0.5 + m = 0.670820393 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 = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.670820393 + -0.5 m = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 m = 0.170820393 Simplifying m = 0.170820393Subproblem 2
m + 0.5 = -0.670820393 Simplifying m + 0.5 = -0.670820393 Reorder the terms: 0.5 + m = -0.670820393 Solving 0.5 + m = -0.670820393 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 = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.670820393 + -0.5 m = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 m = -1.170820393 Simplifying m = -1.170820393Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.170820393, -1.170820393}
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