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Simplifying m2 + -4m + -32 = 32 Reorder the terms: -32 + -4m + m2 = 32 Solving -32 + -4m + m2 = 32 Solving for variable 'm'. Reorder the terms: -32 + -32 + -4m + m2 = 32 + -32 Combine like terms: -32 + -32 = -64 -64 + -4m + m2 = 32 + -32 Combine like terms: 32 + -32 = 0 -64 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -4m + 64 + m2 = 0 + 64 Reorder the terms: -64 + 64 + -4m + m2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -4m + m2 = 0 + 64 -4m + m2 = 0 + 64 Combine like terms: 0 + 64 = 64 -4m + m2 = 64 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 = 64 + 4 Reorder the terms: 4 + -4m + m2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + -4m + m2 = 68 Factor a perfect square on the left side: (m + -2)(m + -2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (m + -2) equal to 8.246211251 and -8.246211251.Subproblem 1
m + -2 = 8.246211251 Simplifying m + -2 = 8.246211251 Reorder the terms: -2 + m = 8.246211251 Solving -2 + m = 8.246211251 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 = 8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + m = 8.246211251 + 2 m = 8.246211251 + 2 Combine like terms: 8.246211251 + 2 = 10.246211251 m = 10.246211251 Simplifying m = 10.246211251Subproblem 2
m + -2 = -8.246211251 Simplifying m + -2 = -8.246211251 Reorder the terms: -2 + m = -8.246211251 Solving -2 + m = -8.246211251 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 = -8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + m = -8.246211251 + 2 m = -8.246211251 + 2 Combine like terms: -8.246211251 + 2 = -6.246211251 m = -6.246211251 Simplifying m = -6.246211251Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.246211251, -6.246211251}
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