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Simplifying 9m2 + 18m + -8 = 5 Reorder the terms: -8 + 18m + 9m2 = 5 Solving -8 + 18m + 9m2 = 5 Solving for variable 'm'. Reorder the terms: -8 + -5 + 18m + 9m2 = 5 + -5 Combine like terms: -8 + -5 = -13 -13 + 18m + 9m2 = 5 + -5 Combine like terms: 5 + -5 = 0 -13 + 18m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + 2m + m2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + 2m + 1.444444444 + m2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + 2m + m2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + 2m + m2 = 0 + 1.444444444 2m + m2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 2m + m2 = 1.444444444 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 = 1.444444444 + 1 Reorder the terms: 1 + 2m + m2 = 1.444444444 + 1 Combine like terms: 1.444444444 + 1 = 2.444444444 1 + 2m + m2 = 2.444444444 Factor a perfect square on the left side: (m + 1)(m + 1) = 2.444444444 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (m + 1) equal to 1.56347192 and -1.56347192.Subproblem 1
m + 1 = 1.56347192 Simplifying m + 1 = 1.56347192 Reorder the terms: 1 + m = 1.56347192 Solving 1 + m = 1.56347192 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 = 1.56347192 + -1 Combine like terms: 1 + -1 = 0 0 + m = 1.56347192 + -1 m = 1.56347192 + -1 Combine like terms: 1.56347192 + -1 = 0.56347192 m = 0.56347192 Simplifying m = 0.56347192Subproblem 2
m + 1 = -1.56347192 Simplifying m + 1 = -1.56347192 Reorder the terms: 1 + m = -1.56347192 Solving 1 + m = -1.56347192 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 = -1.56347192 + -1 Combine like terms: 1 + -1 = 0 0 + m = -1.56347192 + -1 m = -1.56347192 + -1 Combine like terms: -1.56347192 + -1 = -2.56347192 m = -2.56347192 Simplifying m = -2.56347192Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.56347192, -2.56347192}
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