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Simplifying (m4) + (5m3) + -1(35m2) = 0 m4 + (5m3) + -1(35m2) = 0 Remove parenthesis around (35m2) m4 + (5m3) + -1 * 35m2 = 0 Multiply -1 * 35 m4 + (5m3) + -35m2 = 0 Reorder the terms: -35m2 + (5m3) + m4 = 0 Solving -35m2 + (5m3) + m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(-35 + (5m) + m2) = 0Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(-35 + (5m) + m2)' equal to zero and attempt to solve: Simplifying -35 + (5m) + m2 = 0 Solving -35 + (5m) + m2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + (5m) + 35 + m2 = 0 + 35 Reorder the terms: -35 + 35 + (5m) + m2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + (5m) + m2 = 0 + 35 (5m) + m2 = 0 + 35 Combine like terms: 0 + 35 = 35 (5m) + m2 = 35 The m term is (5m). Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. (5m) + 6.25 + m2 = 35 + 6.25 Reorder the terms: 6.25 + (5m) + m2 = 35 + 6.25 Combine like terms: 35 + 6.25 = 41.25 6.25 + (5m) + m2 = 41.25 Factor a perfect square on the left side: (m + 2.5)(m + 2.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (m + 2.5) equal to 6.422616289 and -6.422616289.Subproblem 1
m + 2.5 = 6.422616289 Simplifying m + 2.5 = 6.422616289 Reorder the terms: 2.5 + m = 6.422616289 Solving 2.5 + m = 6.422616289 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 6.422616289 + -2.5 m = 6.422616289 + -2.5 Combine like terms: 6.422616289 + -2.5 = 3.922616289 m = 3.922616289 Simplifying m = 3.922616289Subproblem 2
m + 2.5 = -6.422616289 Simplifying m + 2.5 = -6.422616289 Reorder the terms: 2.5 + m = -6.422616289 Solving 2.5 + m = -6.422616289 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -6.422616289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -6.422616289 + -2.5 m = -6.422616289 + -2.5 Combine like terms: -6.422616289 + -2.5 = -8.922616289 m = -8.922616289 Simplifying m = -8.922616289Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.922616289, -8.922616289}Solution
m = {0, 3.922616289, -8.922616289}
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