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Simplifying -81m4 + -45m3 + 9m2 = 0 Reorder the terms: 9m2 + -45m3 + -81m4 = 0 Solving 9m2 + -45m3 + -81m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '9m2'. 9m2(1 + -5m + -9m2) = 0 Ignore the factor 9.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 '(1 + -5m + -9m2)' equal to zero and attempt to solve: Simplifying 1 + -5m + -9m2 = 0 Solving 1 + -5m + -9m2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + 0.5555555556m + m2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.5555555556m + 0.1111111111 + m2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.5555555556m + m2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.5555555556m + m2 = 0 + 0.1111111111 0.5555555556m + m2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.5555555556m + m2 = 0.1111111111 The m term is 0.5555555556m. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556m + 0.07716049384 + m2 = 0.1111111111 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556m + m2 = 0.1111111111 + 0.07716049384 Combine like terms: 0.1111111111 + 0.07716049384 = 0.18827160494 0.07716049384 + 0.5555555556m + m2 = 0.18827160494 Factor a perfect square on the left side: (m + 0.2777777778)(m + 0.2777777778) = 0.18827160494 Calculate the square root of the right side: 0.43390276 Break this problem into two subproblems by setting (m + 0.2777777778) equal to 0.43390276 and -0.43390276.Subproblem 1
m + 0.2777777778 = 0.43390276 Simplifying m + 0.2777777778 = 0.43390276 Reorder the terms: 0.2777777778 + m = 0.43390276 Solving 0.2777777778 + m = 0.43390276 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + m = 0.43390276 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + m = 0.43390276 + -0.2777777778 m = 0.43390276 + -0.2777777778 Combine like terms: 0.43390276 + -0.2777777778 = 0.1561249822 m = 0.1561249822 Simplifying m = 0.1561249822Subproblem 2
m + 0.2777777778 = -0.43390276 Simplifying m + 0.2777777778 = -0.43390276 Reorder the terms: 0.2777777778 + m = -0.43390276 Solving 0.2777777778 + m = -0.43390276 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + m = -0.43390276 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + m = -0.43390276 + -0.2777777778 m = -0.43390276 + -0.2777777778 Combine like terms: -0.43390276 + -0.2777777778 = -0.7116805378 m = -0.7116805378 Simplifying m = -0.7116805378Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1561249822, -0.7116805378}Solution
m = {0, 0.1561249822, -0.7116805378}
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