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Simplifying m2 + -8m + -79 = 8 Reorder the terms: -79 + -8m + m2 = 8 Solving -79 + -8m + m2 = 8 Solving for variable 'm'. Reorder the terms: -79 + -8 + -8m + m2 = 8 + -8 Combine like terms: -79 + -8 = -87 -87 + -8m + m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -87 + -8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + -8m + 87 + m2 = 0 + 87 Reorder the terms: -87 + 87 + -8m + m2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + -8m + m2 = 0 + 87 -8m + m2 = 0 + 87 Combine like terms: 0 + 87 = 87 -8m + m2 = 87 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = 87 + 16 Reorder the terms: 16 + -8m + m2 = 87 + 16 Combine like terms: 87 + 16 = 103 16 + -8m + m2 = 103 Factor a perfect square on the left side: (m + -4)(m + -4) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (m + -4) equal to 10.148891565 and -10.148891565.Subproblem 1
m + -4 = 10.148891565 Simplifying m + -4 = 10.148891565 Reorder the terms: -4 + m = 10.148891565 Solving -4 + m = 10.148891565 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 10.148891565 + 4 Combine like terms: -4 + 4 = 0 0 + m = 10.148891565 + 4 m = 10.148891565 + 4 Combine like terms: 10.148891565 + 4 = 14.148891565 m = 14.148891565 Simplifying m = 14.148891565Subproblem 2
m + -4 = -10.148891565 Simplifying m + -4 = -10.148891565 Reorder the terms: -4 + m = -10.148891565 Solving -4 + m = -10.148891565 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -10.148891565 + 4 Combine like terms: -4 + 4 = 0 0 + m = -10.148891565 + 4 m = -10.148891565 + 4 Combine like terms: -10.148891565 + 4 = -6.148891565 m = -6.148891565 Simplifying m = -6.148891565Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.148891565, -6.148891565}
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