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Simplifying 7m2 + -16m + -8 = 0 Reorder the terms: -8 + -16m + 7m2 = 0 Solving -8 + -16m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -2.285714286m + m2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -2.285714286m + 1.142857143 + m2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -2.285714286m + m2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -2.285714286m + m2 = 0 + 1.142857143 -2.285714286m + m2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -2.285714286m + m2 = 1.142857143 The m term is -2.285714286m. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286m + 1.306122449 + m2 = 1.142857143 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286m + m2 = 1.142857143 + 1.306122449 Combine like terms: 1.142857143 + 1.306122449 = 2.448979592 1.306122449 + -2.285714286m + m2 = 2.448979592 Factor a perfect square on the left side: (m + -1.142857143)(m + -1.142857143) = 2.448979592 Calculate the square root of the right side: 1.564921593 Break this problem into two subproblems by setting (m + -1.142857143) equal to 1.564921593 and -1.564921593.Subproblem 1
m + -1.142857143 = 1.564921593 Simplifying m + -1.142857143 = 1.564921593 Reorder the terms: -1.142857143 + m = 1.564921593 Solving -1.142857143 + m = 1.564921593 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + m = 1.564921593 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + m = 1.564921593 + 1.142857143 m = 1.564921593 + 1.142857143 Combine like terms: 1.564921593 + 1.142857143 = 2.707778736 m = 2.707778736 Simplifying m = 2.707778736Subproblem 2
m + -1.142857143 = -1.564921593 Simplifying m + -1.142857143 = -1.564921593 Reorder the terms: -1.142857143 + m = -1.564921593 Solving -1.142857143 + m = -1.564921593 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + m = -1.564921593 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + m = -1.564921593 + 1.142857143 m = -1.564921593 + 1.142857143 Combine like terms: -1.564921593 + 1.142857143 = -0.42206445 m = -0.42206445 Simplifying m = -0.42206445Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.707778736, -0.42206445}
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