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Simplifying 9m(4m + -8) = 53 Reorder the terms: 9m(-8 + 4m) = 53 (-8 * 9m + 4m * 9m) = 53 (-72m + 36m2) = 53 Solving -72m + 36m2 = 53 Solving for variable 'm'. Reorder the terms: -53 + -72m + 36m2 = 53 + -53 Combine like terms: 53 + -53 = 0 -53 + -72m + 36m2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.472222222 + -2m + m2 = 0 Move the constant term to the right: Add '1.472222222' to each side of the equation. -1.472222222 + -2m + 1.472222222 + m2 = 0 + 1.472222222 Reorder the terms: -1.472222222 + 1.472222222 + -2m + m2 = 0 + 1.472222222 Combine like terms: -1.472222222 + 1.472222222 = 0.000000000 0.000000000 + -2m + m2 = 0 + 1.472222222 -2m + m2 = 0 + 1.472222222 Combine like terms: 0 + 1.472222222 = 1.472222222 -2m + m2 = 1.472222222 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 = 1.472222222 + 1 Reorder the terms: 1 + -2m + m2 = 1.472222222 + 1 Combine like terms: 1.472222222 + 1 = 2.472222222 1 + -2m + m2 = 2.472222222 Factor a perfect square on the left side: (m + -1)(m + -1) = 2.472222222 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (m + -1) equal to 1.572330189 and -1.572330189.Subproblem 1
m + -1 = 1.572330189 Simplifying m + -1 = 1.572330189 Reorder the terms: -1 + m = 1.572330189 Solving -1 + m = 1.572330189 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 = 1.572330189 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.572330189 + 1 m = 1.572330189 + 1 Combine like terms: 1.572330189 + 1 = 2.572330189 m = 2.572330189 Simplifying m = 2.572330189Subproblem 2
m + -1 = -1.572330189 Simplifying m + -1 = -1.572330189 Reorder the terms: -1 + m = -1.572330189 Solving -1 + m = -1.572330189 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 = -1.572330189 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.572330189 + 1 m = -1.572330189 + 1 Combine like terms: -1.572330189 + 1 = -0.572330189 m = -0.572330189 Simplifying m = -0.572330189Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.572330189, -0.572330189}
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