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Simplifying 3m2 + -8m + -57 = 3 + 4m Reorder the terms: -57 + -8m + 3m2 = 3 + 4m Solving -57 + -8m + 3m2 = 3 + 4m Solving for variable 'm'. Reorder the terms: -57 + -3 + -8m + -4m + 3m2 = 3 + 4m + -3 + -4m Combine like terms: -57 + -3 = -60 -60 + -8m + -4m + 3m2 = 3 + 4m + -3 + -4m Combine like terms: -8m + -4m = -12m -60 + -12m + 3m2 = 3 + 4m + -3 + -4m Reorder the terms: -60 + -12m + 3m2 = 3 + -3 + 4m + -4m Combine like terms: 3 + -3 = 0 -60 + -12m + 3m2 = 0 + 4m + -4m -60 + -12m + 3m2 = 4m + -4m Combine like terms: 4m + -4m = 0 -60 + -12m + 3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + -4m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-20 + -4m + m2)' equal to zero and attempt to solve: Simplifying -20 + -4m + m2 = 0 Solving -20 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -4m + 20 + m2 = 0 + 20 Reorder the terms: -20 + 20 + -4m + m2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4m + m2 = 0 + 20 -4m + m2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4m + m2 = 20 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 20 + 4 Reorder the terms: 4 + -4m + m2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4m + m2 = 24 Factor a perfect square on the left side: (m + -2)(m + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (m + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
m + -2 = 4.898979486 Simplifying m + -2 = 4.898979486 Reorder the terms: -2 + m = 4.898979486 Solving -2 + m = 4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + m = 4.898979486 + 2 m = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 m = 6.898979486 Simplifying m = 6.898979486Subproblem 2
m + -2 = -4.898979486 Simplifying m + -2 = -4.898979486 Reorder the terms: -2 + m = -4.898979486 Solving -2 + m = -4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + m = -4.898979486 + 2 m = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 m = -2.898979486 Simplifying m = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.898979486, -2.898979486}Solution
m = {6.898979486, -2.898979486}
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