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Simplifying 9m3 + -7m4 + 8m2 = 0 Reorder the terms: 8m2 + 9m3 + -7m4 = 0 Solving 8m2 + 9m3 + -7m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(8 + 9m + -7m2) = 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 '(8 + 9m + -7m2)' equal to zero and attempt to solve: Simplifying 8 + 9m + -7m2 = 0 Solving 8 + 9m + -7m2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1.142857143 + -1.285714286m + m2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -1.285714286m + 1.142857143 + m2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -1.285714286m + m2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -1.285714286m + m2 = 0 + 1.142857143 -1.285714286m + m2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -1.285714286m + m2 = 1.142857143 The m term is -1.285714286m. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286m + 0.4132653063 + m2 = 1.142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286m + m2 = 1.142857143 + 0.4132653063 Combine like terms: 1.142857143 + 0.4132653063 = 1.5561224493 0.4132653063 + -1.285714286m + m2 = 1.5561224493 Factor a perfect square on the left side: (m + -0.642857143)(m + -0.642857143) = 1.5561224493 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (m + -0.642857143) equal to 1.247446371 and -1.247446371.Subproblem 1
m + -0.642857143 = 1.247446371 Simplifying m + -0.642857143 = 1.247446371 Reorder the terms: -0.642857143 + m = 1.247446371 Solving -0.642857143 + m = 1.247446371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + m = 1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + m = 1.247446371 + 0.642857143 m = 1.247446371 + 0.642857143 Combine like terms: 1.247446371 + 0.642857143 = 1.890303514 m = 1.890303514 Simplifying m = 1.890303514Subproblem 2
m + -0.642857143 = -1.247446371 Simplifying m + -0.642857143 = -1.247446371 Reorder the terms: -0.642857143 + m = -1.247446371 Solving -0.642857143 + m = -1.247446371 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + m = -1.247446371 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + m = -1.247446371 + 0.642857143 m = -1.247446371 + 0.642857143 Combine like terms: -1.247446371 + 0.642857143 = -0.604589228 m = -0.604589228 Simplifying m = -0.604589228Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.890303514, -0.604589228}Solution
m = {0, 1.890303514, -0.604589228}
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