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Simplifying m2 + 19m + 14 = 0 Reorder the terms: 14 + 19m + m2 = 0 Solving 14 + 19m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 19m + -14 + m2 = 0 + -14 Reorder the terms: 14 + -14 + 19m + m2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 19m + m2 = 0 + -14 19m + m2 = 0 + -14 Combine like terms: 0 + -14 = -14 19m + m2 = -14 The m term is 19m. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19m + 90.25 + m2 = -14 + 90.25 Reorder the terms: 90.25 + 19m + m2 = -14 + 90.25 Combine like terms: -14 + 90.25 = 76.25 90.25 + 19m + m2 = 76.25 Factor a perfect square on the left side: (m + 9.5)(m + 9.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (m + 9.5) equal to 8.732124598 and -8.732124598.Subproblem 1
m + 9.5 = 8.732124598 Simplifying m + 9.5 = 8.732124598 Reorder the terms: 9.5 + m = 8.732124598 Solving 9.5 + m = 8.732124598 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + m = 8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + m = 8.732124598 + -9.5 m = 8.732124598 + -9.5 Combine like terms: 8.732124598 + -9.5 = -0.767875402 m = -0.767875402 Simplifying m = -0.767875402Subproblem 2
m + 9.5 = -8.732124598 Simplifying m + 9.5 = -8.732124598 Reorder the terms: 9.5 + m = -8.732124598 Solving 9.5 + m = -8.732124598 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + m = -8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + m = -8.732124598 + -9.5 m = -8.732124598 + -9.5 Combine like terms: -8.732124598 + -9.5 = -18.232124598 m = -18.232124598 Simplifying m = -18.232124598Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.767875402, -18.232124598}
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