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Simplifying 6m2 + -60m + 10 = 0 Reorder the terms: 10 + -60m + 6m2 = 0 Solving 10 + -60m + 6m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -30m + 3m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -30m + 3m2)' equal to zero and attempt to solve: Simplifying 5 + -30m + 3m2 = 0 Solving 5 + -30m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -10m + m2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -10m + -1.666666667 + m2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -10m + m2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -10m + m2 = 0 + -1.666666667 -10m + m2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -10m + m2 = -1.666666667 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = -1.666666667 + 25 Reorder the terms: 25 + -10m + m2 = -1.666666667 + 25 Combine like terms: -1.666666667 + 25 = 23.333333333 25 + -10m + m2 = 23.333333333 Factor a perfect square on the left side: (m + -5)(m + -5) = 23.333333333 Calculate the square root of the right side: 4.830458915 Break this problem into two subproblems by setting (m + -5) equal to 4.830458915 and -4.830458915.Subproblem 1
m + -5 = 4.830458915 Simplifying m + -5 = 4.830458915 Reorder the terms: -5 + m = 4.830458915 Solving -5 + m = 4.830458915 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 4.830458915 + 5 Combine like terms: -5 + 5 = 0 0 + m = 4.830458915 + 5 m = 4.830458915 + 5 Combine like terms: 4.830458915 + 5 = 9.830458915 m = 9.830458915 Simplifying m = 9.830458915Subproblem 2
m + -5 = -4.830458915 Simplifying m + -5 = -4.830458915 Reorder the terms: -5 + m = -4.830458915 Solving -5 + m = -4.830458915 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -4.830458915 + 5 Combine like terms: -5 + 5 = 0 0 + m = -4.830458915 + 5 m = -4.830458915 + 5 Combine like terms: -4.830458915 + 5 = 0.169541085 m = 0.169541085 Simplifying m = 0.169541085Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.830458915, 0.169541085}Solution
m = {9.830458915, 0.169541085}
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