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Simplifying 3m4 + 18m3 + -162m2 = 0 Reorder the terms: -162m2 + 18m3 + 3m4 = 0 Solving -162m2 + 18m3 + 3m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m2'. 3m2(-54 + 6m + m2) = 0 Ignore the factor 3.Subproblem 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 '(-54 + 6m + m2)' equal to zero and attempt to solve: Simplifying -54 + 6m + m2 = 0 Solving -54 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 6m + 54 + m2 = 0 + 54 Reorder the terms: -54 + 54 + 6m + m2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 6m + m2 = 0 + 54 6m + m2 = 0 + 54 Combine like terms: 0 + 54 = 54 6m + m2 = 54 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = 54 + 9 Reorder the terms: 9 + 6m + m2 = 54 + 9 Combine like terms: 54 + 9 = 63 9 + 6m + m2 = 63 Factor a perfect square on the left side: (m + 3)(m + 3) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (m + 3) equal to 7.937253933 and -7.937253933.Subproblem 1
m + 3 = 7.937253933 Simplifying m + 3 = 7.937253933 Reorder the terms: 3 + m = 7.937253933 Solving 3 + m = 7.937253933 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + m = 7.937253933 + -3 m = 7.937253933 + -3 Combine like terms: 7.937253933 + -3 = 4.937253933 m = 4.937253933 Simplifying m = 4.937253933Subproblem 2
m + 3 = -7.937253933 Simplifying m + 3 = -7.937253933 Reorder the terms: 3 + m = -7.937253933 Solving 3 + m = -7.937253933 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + m = -7.937253933 + -3 m = -7.937253933 + -3 Combine like terms: -7.937253933 + -3 = -10.937253933 m = -10.937253933 Simplifying m = -10.937253933Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.937253933, -10.937253933}Solution
m = {0, 4.937253933, -10.937253933}
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