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Simplifying 8m2 + 24m + -95 = -4 Reorder the terms: -95 + 24m + 8m2 = -4 Solving -95 + 24m + 8m2 = -4 Solving for variable 'm'. Reorder the terms: -95 + 4 + 24m + 8m2 = -4 + 4 Combine like terms: -95 + 4 = -91 -91 + 24m + 8m2 = -4 + 4 Combine like terms: -4 + 4 = 0 -91 + 24m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.375 + 3m + m2 = 0 Move the constant term to the right: Add '11.375' to each side of the equation. -11.375 + 3m + 11.375 + m2 = 0 + 11.375 Reorder the terms: -11.375 + 11.375 + 3m + m2 = 0 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + 3m + m2 = 0 + 11.375 3m + m2 = 0 + 11.375 Combine like terms: 0 + 11.375 = 11.375 3m + m2 = 11.375 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 11.375 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 11.375 + 2.25 Combine like terms: 11.375 + 2.25 = 13.625 2.25 + 3m + m2 = 13.625 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 13.625 Calculate the square root of the right side: 3.691205765 Break this problem into two subproblems by setting (m + 1.5) equal to 3.691205765 and -3.691205765.Subproblem 1
m + 1.5 = 3.691205765 Simplifying m + 1.5 = 3.691205765 Reorder the terms: 1.5 + m = 3.691205765 Solving 1.5 + m = 3.691205765 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 3.691205765 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 3.691205765 + -1.5 m = 3.691205765 + -1.5 Combine like terms: 3.691205765 + -1.5 = 2.191205765 m = 2.191205765 Simplifying m = 2.191205765Subproblem 2
m + 1.5 = -3.691205765 Simplifying m + 1.5 = -3.691205765 Reorder the terms: 1.5 + m = -3.691205765 Solving 1.5 + m = -3.691205765 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -3.691205765 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -3.691205765 + -1.5 m = -3.691205765 + -1.5 Combine like terms: -3.691205765 + -1.5 = -5.191205765 m = -5.191205765 Simplifying m = -5.191205765Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.191205765, -5.191205765}
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