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Simplifying 5m2 + 17m + -66 = 0 Reorder the terms: -66 + 17m + 5m2 = 0 Solving -66 + 17m + 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'. -13.2 + 3.4m + m2 = 0 Move the constant term to the right: Add '13.2' to each side of the equation. -13.2 + 3.4m + 13.2 + m2 = 0 + 13.2 Reorder the terms: -13.2 + 13.2 + 3.4m + m2 = 0 + 13.2 Combine like terms: -13.2 + 13.2 = 0.0 0.0 + 3.4m + m2 = 0 + 13.2 3.4m + m2 = 0 + 13.2 Combine like terms: 0 + 13.2 = 13.2 3.4m + m2 = 13.2 The m term is 3.4m. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4m + 2.89 + m2 = 13.2 + 2.89 Reorder the terms: 2.89 + 3.4m + m2 = 13.2 + 2.89 Combine like terms: 13.2 + 2.89 = 16.09 2.89 + 3.4m + m2 = 16.09 Factor a perfect square on the left side: (m + 1.7)(m + 1.7) = 16.09 Calculate the square root of the right side: 4.011234224 Break this problem into two subproblems by setting (m + 1.7) equal to 4.011234224 and -4.011234224.Subproblem 1
m + 1.7 = 4.011234224 Simplifying m + 1.7 = 4.011234224 Reorder the terms: 1.7 + m = 4.011234224 Solving 1.7 + m = 4.011234224 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + m = 4.011234224 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + m = 4.011234224 + -1.7 m = 4.011234224 + -1.7 Combine like terms: 4.011234224 + -1.7 = 2.311234224 m = 2.311234224 Simplifying m = 2.311234224Subproblem 2
m + 1.7 = -4.011234224 Simplifying m + 1.7 = -4.011234224 Reorder the terms: 1.7 + m = -4.011234224 Solving 1.7 + m = -4.011234224 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + m = -4.011234224 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + m = -4.011234224 + -1.7 m = -4.011234224 + -1.7 Combine like terms: -4.011234224 + -1.7 = -5.711234224 m = -5.711234224 Simplifying m = -5.711234224Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.311234224, -5.711234224}
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