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Simplifying -4m + m2 = 99 Solving -4m + m2 = 99 Solving for variable 'm'. Reorder the terms: -99 + -4m + m2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -4m + 99 + m2 = 0 + 99 Reorder the terms: -99 + 99 + -4m + m2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -4m + m2 = 0 + 99 -4m + m2 = 0 + 99 Combine like terms: 0 + 99 = 99 -4m + m2 = 99 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 99 + 4 Reorder the terms: 4 + -4m + m2 = 99 + 4 Combine like terms: 99 + 4 = 103 4 + -4m + m2 = 103 Factor a perfect square on the left side: (m + -2)(m + -2) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (m + -2) equal to 10.148891565 and -10.148891565.Subproblem 1
m + -2 = 10.148891565 Simplifying m + -2 = 10.148891565 Reorder the terms: -2 + m = 10.148891565 Solving -2 + m = 10.148891565 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 10.148891565 + 2 Combine like terms: -2 + 2 = 0 0 + m = 10.148891565 + 2 m = 10.148891565 + 2 Combine like terms: 10.148891565 + 2 = 12.148891565 m = 12.148891565 Simplifying m = 12.148891565Subproblem 2
m + -2 = -10.148891565 Simplifying m + -2 = -10.148891565 Reorder the terms: -2 + m = -10.148891565 Solving -2 + m = -10.148891565 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -10.148891565 + 2 Combine like terms: -2 + 2 = 0 0 + m = -10.148891565 + 2 m = -10.148891565 + 2 Combine like terms: -10.148891565 + 2 = -8.148891565 m = -8.148891565 Simplifying m = -8.148891565Solution
The solution to the problem is based on the solutions from the subproblems. m = {12.148891565, -8.148891565}
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