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Simplifying 63x4 + -14x3 + 35x2 = 0 Reorder the terms: 35x2 + -14x3 + 63x4 = 0 Solving 35x2 + -14x3 + 63x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x2'. 7x2(5 + -2x + 9x2) = 0 Ignore the factor 7.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 '(5 + -2x + 9x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + 9x2 = 0 Solving 5 + -2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -0.2222222222x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -0.2222222222x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -0.2222222222x + x2 = 0 + -0.5555555556 -0.2222222222x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -0.2222222222x + x2 = -0.5555555556 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = -0.5555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = -0.5555555556 + 0.01234567901 Combine like terms: -0.5555555556 + 0.01234567901 = -0.54320987659 0.01234567901 + -0.2222222222x + x2 = -0.54320987659 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = -0.54320987659 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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