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Simplifying 8m2 + 16m + -3 = 6 Reorder the terms: -3 + 16m + 8m2 = 6 Solving -3 + 16m + 8m2 = 6 Solving for variable 'm'. Reorder the terms: -3 + -6 + 16m + 8m2 = 6 + -6 Combine like terms: -3 + -6 = -9 -9 + 16m + 8m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -9 + 16m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 2m + m2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 2m + 1.125 + m2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 2m + m2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 2m + m2 = 0 + 1.125 2m + m2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 2m + m2 = 1.125 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 1.125 + 1 Reorder the terms: 1 + 2m + m2 = 1.125 + 1 Combine like terms: 1.125 + 1 = 2.125 1 + 2m + m2 = 2.125 Factor a perfect square on the left side: (m + 1)(m + 1) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (m + 1) equal to 1.457737974 and -1.457737974.Subproblem 1
m + 1 = 1.457737974 Simplifying m + 1 = 1.457737974 Reorder the terms: 1 + m = 1.457737974 Solving 1 + m = 1.457737974 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 1.457737974 + -1 Combine like terms: 1 + -1 = 0 0 + m = 1.457737974 + -1 m = 1.457737974 + -1 Combine like terms: 1.457737974 + -1 = 0.457737974 m = 0.457737974 Simplifying m = 0.457737974Subproblem 2
m + 1 = -1.457737974 Simplifying m + 1 = -1.457737974 Reorder the terms: 1 + m = -1.457737974 Solving 1 + m = -1.457737974 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -1.457737974 + -1 Combine like terms: 1 + -1 = 0 0 + m = -1.457737974 + -1 m = -1.457737974 + -1 Combine like terms: -1.457737974 + -1 = -2.457737974 m = -2.457737974 Simplifying m = -2.457737974Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.457737974, -2.457737974}
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