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Simplifying 10x7 + -9x5 + -12x3 = 0 Reorder the terms: -12x3 + -9x5 + 10x7 = 0 Solving -12x3 + -9x5 + 10x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(-12 + -9x2 + 10x4) = 0Subproblem 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 '(-12 + -9x2 + 10x4)' equal to zero and attempt to solve: Simplifying -12 + -9x2 + 10x4 = 0 Solving -12 + -9x2 + 10x4 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + -0.9x2 + x4 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.9x2 + 1.2 + x4 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.9x2 + x4 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.9x2 + x4 = 0 + 1.2 -0.9x2 + x4 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.9x2 + x4 = 1.2 The x term is -0.9x2. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x2 + 0.2025 + x4 = 1.2 + 0.2025 Reorder the terms: 0.2025 + -0.9x2 + x4 = 1.2 + 0.2025 Combine like terms: 1.2 + 0.2025 = 1.4025 0.2025 + -0.9x2 + x4 = 1.4025 Factor a perfect square on the left side: (x2 + -0.45)(x2 + -0.45) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (x2 + -0.45) equal to 1.184271928 and -1.184271928.Subproblem 1
x2 + -0.45 = 1.184271928 Simplifying x2 + -0.45 = 1.184271928 Reorder the terms: -0.45 + x2 = 1.184271928 Solving -0.45 + x2 = 1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x2 = 1.184271928 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x2 = 1.184271928 + 0.45 x2 = 1.184271928 + 0.45 Combine like terms: 1.184271928 + 0.45 = 1.634271928 x2 = 1.634271928 Simplifying x2 = 1.634271928 Take the square root of each side: x = {-1.278386455, 1.278386455}Subproblem 2
x2 + -0.45 = -1.184271928 Simplifying x2 + -0.45 = -1.184271928 Reorder the terms: -0.45 + x2 = -1.184271928 Solving -0.45 + x2 = -1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x2 = -1.184271928 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x2 = -1.184271928 + 0.45 x2 = -1.184271928 + 0.45 Combine like terms: -1.184271928 + 0.45 = -0.734271928 x2 = -0.734271928 Simplifying x2 = -0.734271928 Reorder the terms: 0.734271928 + x2 = -0.734271928 + 0.734271928 Combine like terms: -0.734271928 + 0.734271928 = 0.000000000 0.734271928 + x2 = 0.000000000 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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