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Simplifying 4m(m) + -40m + 56 = 0 Multiply m * m 4m2 + -40m + 56 = 0 Reorder the terms: 56 + -40m + 4m2 = 0 Solving 56 + -40m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(14 + -10m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(14 + -10m + m2)' equal to zero and attempt to solve: Simplifying 14 + -10m + m2 = 0 Solving 14 + -10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -10m + -14 + m2 = 0 + -14 Reorder the terms: 14 + -14 + -10m + m2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -10m + m2 = 0 + -14 -10m + m2 = 0 + -14 Combine like terms: 0 + -14 = -14 -10m + m2 = -14 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 = -14 + 25 Reorder the terms: 25 + -10m + m2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + -10m + m2 = 11 Factor a perfect square on the left side: (m + -5)(m + -5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (m + -5) equal to 3.31662479 and -3.31662479.Subproblem 1
m + -5 = 3.31662479 Simplifying m + -5 = 3.31662479 Reorder the terms: -5 + m = 3.31662479 Solving -5 + m = 3.31662479 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 = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + m = 3.31662479 + 5 m = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 m = 8.31662479 Simplifying m = 8.31662479Subproblem 2
m + -5 = -3.31662479 Simplifying m + -5 = -3.31662479 Reorder the terms: -5 + m = -3.31662479 Solving -5 + m = -3.31662479 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 = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + m = -3.31662479 + 5 m = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 m = 1.68337521 Simplifying m = 1.68337521Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.31662479, 1.68337521}Solution
m = {8.31662479, 1.68337521}
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