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Simplifying 42m8 + 36m6 + -60m4 = 0 Reorder the terms: -60m4 + 36m6 + 42m8 = 0 Solving -60m4 + 36m6 + 42m8 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '6m4'. 6m4(-10 + 6m2 + 7m4) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'm4' equal to zero and attempt to solve: Simplifying m4 = 0 Solving m4 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-10 + 6m2 + 7m4)' equal to zero and attempt to solve: Simplifying -10 + 6m2 + 7m4 = 0 Solving -10 + 6m2 + 7m4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 0.8571428571m2 + m4 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.8571428571m2 + 1.428571429 + m4 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.8571428571m2 + m4 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.8571428571m2 + m4 = 0 + 1.428571429 0.8571428571m2 + m4 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.8571428571m2 + m4 = 1.428571429 The m term is 0.8571428571m2. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571m2 + 0.1836734694 + m4 = 1.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571m2 + m4 = 1.428571429 + 0.1836734694 Combine like terms: 1.428571429 + 0.1836734694 = 1.6122448984 0.1836734694 + 0.8571428571m2 + m4 = 1.6122448984 Factor a perfect square on the left side: (m2 + 0.4285714286)(m2 + 0.4285714286) = 1.6122448984 Calculate the square root of the right side: 1.26974206 Break this problem into two subproblems by setting (m2 + 0.4285714286) equal to 1.26974206 and -1.26974206.Subproblem 1
m2 + 0.4285714286 = 1.26974206 Simplifying m2 + 0.4285714286 = 1.26974206 Reorder the terms: 0.4285714286 + m2 = 1.26974206 Solving 0.4285714286 + m2 = 1.26974206 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + m2 = 1.26974206 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + m2 = 1.26974206 + -0.4285714286 m2 = 1.26974206 + -0.4285714286 Combine like terms: 1.26974206 + -0.4285714286 = 0.8411706314 m2 = 0.8411706314 Simplifying m2 = 0.8411706314 Take the square root of each side: m = {-0.917153548, 0.917153548}Subproblem 2
m2 + 0.4285714286 = -1.26974206 Simplifying m2 + 0.4285714286 = -1.26974206 Reorder the terms: 0.4285714286 + m2 = -1.26974206 Solving 0.4285714286 + m2 = -1.26974206 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + m2 = -1.26974206 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + m2 = -1.26974206 + -0.4285714286 m2 = -1.26974206 + -0.4285714286 Combine like terms: -1.26974206 + -0.4285714286 = -1.6983134886 m2 = -1.6983134886 Simplifying m2 = -1.6983134886 Reorder the terms: 1.6983134886 + m2 = -1.6983134886 + 1.6983134886 Combine like terms: -1.6983134886 + 1.6983134886 = 0.0000000000 1.6983134886 + m2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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