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Simplifying 2m2 + 10m + 5 = 0 Reorder the terms: 5 + 10m + 2m2 = 0 Solving 5 + 10m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 5m + m2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 5m + -2.5 + m2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 5m + m2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 5m + m2 = 0 + -2.5 5m + m2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 5m + m2 = -2.5 The m term is 5m. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5m + 6.25 + m2 = -2.5 + 6.25 Reorder the terms: 6.25 + 5m + m2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + 5m + m2 = 3.75 Factor a perfect square on the left side: (m + 2.5)(m + 2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (m + 2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
m + 2.5 = 1.936491673 Simplifying m + 2.5 = 1.936491673 Reorder the terms: 2.5 + m = 1.936491673 Solving 2.5 + m = 1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 1.936491673 + -2.5 m = 1.936491673 + -2.5 Combine like terms: 1.936491673 + -2.5 = -0.563508327 m = -0.563508327 Simplifying m = -0.563508327Subproblem 2
m + 2.5 = -1.936491673 Simplifying m + 2.5 = -1.936491673 Reorder the terms: 2.5 + m = -1.936491673 Solving 2.5 + m = -1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -1.936491673 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -1.936491673 + -2.5 m = -1.936491673 + -2.5 Combine like terms: -1.936491673 + -2.5 = -4.436491673 m = -4.436491673 Simplifying m = -4.436491673Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.563508327, -4.436491673}
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