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Simplifying 10x6 + -15x4 + 35x2 = 0 Reorder the terms: 35x2 + -15x4 + 10x6 = 0 Solving 35x2 + -15x4 + 10x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(7 + -3x2 + 2x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(7 + -3x2 + 2x4)' equal to zero and attempt to solve: Simplifying 7 + -3x2 + 2x4 = 0 Solving 7 + -3x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -1.5x2 + x4 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -1.5x2 + -3.5 + x4 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -1.5x2 + x4 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1.5x2 + x4 = 0 + -3.5 -1.5x2 + x4 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -1.5x2 + x4 = -3.5 The x term is -1.5x2. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x2 + 0.5625 + x4 = -3.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x2 + x4 = -3.5 + 0.5625 Combine like terms: -3.5 + 0.5625 = -2.9375 0.5625 + -1.5x2 + x4 = -2.9375 Factor a perfect square on the left side: (x2 + -0.75)(x2 + -0.75) = -2.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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