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Simplifying 0 = 6m2 + -48m + 18 Reorder the terms: 0 = 18 + -48m + 6m2 Solving 0 = 18 + -48m + 6m2 Solving for variable 'm'. Combine like terms: 0 + -18 = -18 -18 + 48m + -6m2 = 18 + -48m + 6m2 + -18 + 48m + -6m2 Reorder the terms: -18 + 48m + -6m2 = 18 + -18 + -48m + 48m + 6m2 + -6m2 Combine like terms: 18 + -18 = 0 -18 + 48m + -6m2 = 0 + -48m + 48m + 6m2 + -6m2 -18 + 48m + -6m2 = -48m + 48m + 6m2 + -6m2 Combine like terms: -48m + 48m = 0 -18 + 48m + -6m2 = 0 + 6m2 + -6m2 -18 + 48m + -6m2 = 6m2 + -6m2 Combine like terms: 6m2 + -6m2 = 0 -18 + 48m + -6m2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 8m + -1m2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 8m + -1m2)' equal to zero and attempt to solve: Simplifying -3 + 8m + -1m2 = 0 Solving -3 + 8m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -8m + m2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8m + -3 + m2 = 0 + -3 Reorder the terms: 3 + -3 + -8m + m2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8m + m2 = 0 + -3 -8m + m2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8m + m2 = -3 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = -3 + 16 Reorder the terms: 16 + -8m + m2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8m + m2 = 13 Factor a perfect square on the left side: (m + -4)(m + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (m + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
m + -4 = 3.605551275 Simplifying m + -4 = 3.605551275 Reorder the terms: -4 + m = 3.605551275 Solving -4 + m = 3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.605551275 + 4 m = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 m = 7.605551275 Simplifying m = 7.605551275Subproblem 2
m + -4 = -3.605551275 Simplifying m + -4 = -3.605551275 Reorder the terms: -4 + m = -3.605551275 Solving -4 + m = -3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.605551275 + 4 m = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 m = 0.394448725 Simplifying m = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.605551275, 0.394448725}Solution
m = {7.605551275, 0.394448725}
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