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Simplifying 56x7 + -48x5 + -40x3 = 0 Reorder the terms: -40x3 + -48x5 + 56x7 = 0 Solving -40x3 + -48x5 + 56x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x3'. 8x3(-5 + -6x2 + 7x4) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(-5 + -6x2 + 7x4)' equal to zero and attempt to solve: Simplifying -5 + -6x2 + 7x4 = 0 Solving -5 + -6x2 + 7x4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.8571428571x2 + x4 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.8571428571x2 + 0.7142857143 + x4 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.8571428571x2 + x4 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.8571428571x2 + x4 = 0 + 0.7142857143 -0.8571428571x2 + x4 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.8571428571x2 + x4 = 0.7142857143 The x term is -0.8571428571x2. 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. -0.8571428571x2 + 0.1836734694 + x4 = 0.7142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x2 + x4 = 0.7142857143 + 0.1836734694 Combine like terms: 0.7142857143 + 0.1836734694 = 0.8979591837 0.1836734694 + -0.8571428571x2 + x4 = 0.8979591837 Factor a perfect square on the left side: (x2 + -0.4285714286)(x2 + -0.4285714286) = 0.8979591837 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (x2 + -0.4285714286) equal to 0.947607083 and -0.947607083.Subproblem 1
x2 + -0.4285714286 = 0.947607083 Simplifying x2 + -0.4285714286 = 0.947607083 Reorder the terms: -0.4285714286 + x2 = 0.947607083 Solving -0.4285714286 + x2 = 0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x2 = 0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = 0.947607083 + 0.4285714286 x2 = 0.947607083 + 0.4285714286 Combine like terms: 0.947607083 + 0.4285714286 = 1.3761785116 x2 = 1.3761785116 Simplifying x2 = 1.3761785116 Take the square root of each side: x = {-1.173106351, 1.173106351}Subproblem 2
x2 + -0.4285714286 = -0.947607083 Simplifying x2 + -0.4285714286 = -0.947607083 Reorder the terms: -0.4285714286 + x2 = -0.947607083 Solving -0.4285714286 + x2 = -0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x2 = -0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x2 = -0.947607083 + 0.4285714286 x2 = -0.947607083 + 0.4285714286 Combine like terms: -0.947607083 + 0.4285714286 = -0.5190356544 x2 = -0.5190356544 Simplifying x2 = -0.5190356544 Reorder the terms: 0.5190356544 + x2 = -0.5190356544 + 0.5190356544 Combine like terms: -0.5190356544 + 0.5190356544 = 0.0000000000 0.5190356544 + x2 = 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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