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Simplifying m2 + -16m + -84 = 0 Reorder the terms: -84 + -16m + m2 = 0 Solving -84 + -16m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -16m + 84 + m2 = 0 + 84 Reorder the terms: -84 + 84 + -16m + m2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -16m + m2 = 0 + 84 -16m + m2 = 0 + 84 Combine like terms: 0 + 84 = 84 -16m + m2 = 84 The m term is -16m. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16m + 64 + m2 = 84 + 64 Reorder the terms: 64 + -16m + m2 = 84 + 64 Combine like terms: 84 + 64 = 148 64 + -16m + m2 = 148 Factor a perfect square on the left side: (m + -8)(m + -8) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (m + -8) equal to 12.165525061 and -12.165525061.Subproblem 1
m + -8 = 12.165525061 Simplifying m + -8 = 12.165525061 Reorder the terms: -8 + m = 12.165525061 Solving -8 + m = 12.165525061 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m = 12.165525061 + 8 Combine like terms: -8 + 8 = 0 0 + m = 12.165525061 + 8 m = 12.165525061 + 8 Combine like terms: 12.165525061 + 8 = 20.165525061 m = 20.165525061 Simplifying m = 20.165525061Subproblem 2
m + -8 = -12.165525061 Simplifying m + -8 = -12.165525061 Reorder the terms: -8 + m = -12.165525061 Solving -8 + m = -12.165525061 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m = -12.165525061 + 8 Combine like terms: -8 + 8 = 0 0 + m = -12.165525061 + 8 m = -12.165525061 + 8 Combine like terms: -12.165525061 + 8 = -4.165525061 m = -4.165525061 Simplifying m = -4.165525061Solution
The solution to the problem is based on the solutions from the subproblems. m = {20.165525061, -4.165525061}
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