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Simplifying 324 + -43m + m2 = 0 Solving 324 + -43m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-324' to each side of the equation. 324 + -43m + -324 + m2 = 0 + -324 Reorder the terms: 324 + -324 + -43m + m2 = 0 + -324 Combine like terms: 324 + -324 = 0 0 + -43m + m2 = 0 + -324 -43m + m2 = 0 + -324 Combine like terms: 0 + -324 = -324 -43m + m2 = -324 The m term is -43m. Take half its coefficient (-21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. -43m + 462.25 + m2 = -324 + 462.25 Reorder the terms: 462.25 + -43m + m2 = -324 + 462.25 Combine like terms: -324 + 462.25 = 138.25 462.25 + -43m + m2 = 138.25 Factor a perfect square on the left side: (m + -21.5)(m + -21.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (m + -21.5) equal to 11.757976016 and -11.757976016.Subproblem 1
m + -21.5 = 11.757976016 Simplifying m + -21.5 = 11.757976016 Reorder the terms: -21.5 + m = 11.757976016 Solving -21.5 + m = 11.757976016 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + m = 11.757976016 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + m = 11.757976016 + 21.5 m = 11.757976016 + 21.5 Combine like terms: 11.757976016 + 21.5 = 33.257976016 m = 33.257976016 Simplifying m = 33.257976016Subproblem 2
m + -21.5 = -11.757976016 Simplifying m + -21.5 = -11.757976016 Reorder the terms: -21.5 + m = -11.757976016 Solving -21.5 + m = -11.757976016 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + m = -11.757976016 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + m = -11.757976016 + 21.5 m = -11.757976016 + 21.5 Combine like terms: -11.757976016 + 21.5 = 9.742023984 m = 9.742023984 Simplifying m = 9.742023984Solution
The solution to the problem is based on the solutions from the subproblems. m = {33.257976016, 9.742023984}
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