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Simplifying 5m2 + -14m + -15 = 0 Reorder the terms: -15 + -14m + 5m2 = 0 Solving -15 + -14m + 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'. -3 + -2.8m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.8m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -2.8m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.8m + m2 = 0 + 3 -2.8m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.8m + m2 = 3 The m term is -2.8m. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8m + 1.96 + m2 = 3 + 1.96 Reorder the terms: 1.96 + -2.8m + m2 = 3 + 1.96 Combine like terms: 3 + 1.96 = 4.96 1.96 + -2.8m + m2 = 4.96 Factor a perfect square on the left side: (m + -1.4)(m + -1.4) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (m + -1.4) equal to 2.227105745 and -2.227105745.Subproblem 1
m + -1.4 = 2.227105745 Simplifying m + -1.4 = 2.227105745 Reorder the terms: -1.4 + m = 2.227105745 Solving -1.4 + m = 2.227105745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + m = 2.227105745 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + m = 2.227105745 + 1.4 m = 2.227105745 + 1.4 Combine like terms: 2.227105745 + 1.4 = 3.627105745 m = 3.627105745 Simplifying m = 3.627105745Subproblem 2
m + -1.4 = -2.227105745 Simplifying m + -1.4 = -2.227105745 Reorder the terms: -1.4 + m = -2.227105745 Solving -1.4 + m = -2.227105745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + m = -2.227105745 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + m = -2.227105745 + 1.4 m = -2.227105745 + 1.4 Combine like terms: -2.227105745 + 1.4 = -0.827105745 m = -0.827105745 Simplifying m = -0.827105745Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.627105745, -0.827105745}
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