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Simplifying 8m2 + 9m + -24 = -2 Reorder the terms: -24 + 9m + 8m2 = -2 Solving -24 + 9m + 8m2 = -2 Solving for variable 'm'. Reorder the terms: -24 + 2 + 9m + 8m2 = -2 + 2 Combine like terms: -24 + 2 = -22 -22 + 9m + 8m2 = -2 + 2 Combine like terms: -2 + 2 = 0 -22 + 9m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.75 + 1.125m + m2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 1.125m + 2.75 + m2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 1.125m + m2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 1.125m + m2 = 0 + 2.75 1.125m + m2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 1.125m + m2 = 2.75 The m term is 1.125m. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125m + 0.31640625 + m2 = 2.75 + 0.31640625 Reorder the terms: 0.31640625 + 1.125m + m2 = 2.75 + 0.31640625 Combine like terms: 2.75 + 0.31640625 = 3.06640625 0.31640625 + 1.125m + m2 = 3.06640625 Factor a perfect square on the left side: (m + 0.5625)(m + 0.5625) = 3.06640625 Calculate the square root of the right side: 1.751115716 Break this problem into two subproblems by setting (m + 0.5625) equal to 1.751115716 and -1.751115716.Subproblem 1
m + 0.5625 = 1.751115716 Simplifying m + 0.5625 = 1.751115716 Reorder the terms: 0.5625 + m = 1.751115716 Solving 0.5625 + m = 1.751115716 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + m = 1.751115716 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + m = 1.751115716 + -0.5625 m = 1.751115716 + -0.5625 Combine like terms: 1.751115716 + -0.5625 = 1.188615716 m = 1.188615716 Simplifying m = 1.188615716Subproblem 2
m + 0.5625 = -1.751115716 Simplifying m + 0.5625 = -1.751115716 Reorder the terms: 0.5625 + m = -1.751115716 Solving 0.5625 + m = -1.751115716 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + m = -1.751115716 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + m = -1.751115716 + -0.5625 m = -1.751115716 + -0.5625 Combine like terms: -1.751115716 + -0.5625 = -2.313615716 m = -2.313615716 Simplifying m = -2.313615716Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.188615716, -2.313615716}
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