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Simplifying 48m2 + -150m + -160 = 0 Reorder the terms: -160 + -150m + 48m2 = 0 Solving -160 + -150m + 48m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -75m + 24m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -75m + 24m2)' equal to zero and attempt to solve: Simplifying -80 + -75m + 24m2 = 0 Solving -80 + -75m + 24m2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -3.333333333 + -3.125m + m2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -3.125m + 3.333333333 + m2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -3.125m + m2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -3.125m + m2 = 0 + 3.333333333 -3.125m + m2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -3.125m + m2 = 3.333333333 The m term is -3.125m. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125m + 2.44140625 + m2 = 3.333333333 + 2.44140625 Reorder the terms: 2.44140625 + -3.125m + m2 = 3.333333333 + 2.44140625 Combine like terms: 3.333333333 + 2.44140625 = 5.774739583 2.44140625 + -3.125m + m2 = 5.774739583 Factor a perfect square on the left side: (m + -1.5625)(m + -1.5625) = 5.774739583 Calculate the square root of the right side: 2.403068784 Break this problem into two subproblems by setting (m + -1.5625) equal to 2.403068784 and -2.403068784.Subproblem 1
m + -1.5625 = 2.403068784 Simplifying m + -1.5625 = 2.403068784 Reorder the terms: -1.5625 + m = 2.403068784 Solving -1.5625 + m = 2.403068784 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + m = 2.403068784 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + m = 2.403068784 + 1.5625 m = 2.403068784 + 1.5625 Combine like terms: 2.403068784 + 1.5625 = 3.965568784 m = 3.965568784 Simplifying m = 3.965568784Subproblem 2
m + -1.5625 = -2.403068784 Simplifying m + -1.5625 = -2.403068784 Reorder the terms: -1.5625 + m = -2.403068784 Solving -1.5625 + m = -2.403068784 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + m = -2.403068784 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + m = -2.403068784 + 1.5625 m = -2.403068784 + 1.5625 Combine like terms: -2.403068784 + 1.5625 = -0.840568784 m = -0.840568784 Simplifying m = -0.840568784Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.965568784, -0.840568784}Solution
m = {3.965568784, -0.840568784}
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