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Simplifying 2m2 + 17m + 10 = 0 Reorder the terms: 10 + 17m + 2m2 = 0 Solving 10 + 17m + 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'. 5 + 8.5m + m2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 8.5m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + 8.5m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8.5m + m2 = 0 + -5 8.5m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 8.5m + m2 = -5 The m term is 8.5m. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5m + 18.0625 + m2 = -5 + 18.0625 Reorder the terms: 18.0625 + 8.5m + m2 = -5 + 18.0625 Combine like terms: -5 + 18.0625 = 13.0625 18.0625 + 8.5m + m2 = 13.0625 Factor a perfect square on the left side: (m + 4.25)(m + 4.25) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (m + 4.25) equal to 3.614208074 and -3.614208074.Subproblem 1
m + 4.25 = 3.614208074 Simplifying m + 4.25 = 3.614208074 Reorder the terms: 4.25 + m = 3.614208074 Solving 4.25 + m = 3.614208074 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = 3.614208074 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = 3.614208074 + -4.25 m = 3.614208074 + -4.25 Combine like terms: 3.614208074 + -4.25 = -0.635791926 m = -0.635791926 Simplifying m = -0.635791926Subproblem 2
m + 4.25 = -3.614208074 Simplifying m + 4.25 = -3.614208074 Reorder the terms: 4.25 + m = -3.614208074 Solving 4.25 + m = -3.614208074 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = -3.614208074 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = -3.614208074 + -4.25 m = -3.614208074 + -4.25 Combine like terms: -3.614208074 + -4.25 = -7.864208074 m = -7.864208074 Simplifying m = -7.864208074Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.635791926, -7.864208074}
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