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Simplifying 30x4 + -60x3 + 60x2 = 0 Reorder the terms: 60x2 + -60x3 + 30x4 = 0 Solving 60x2 + -60x3 + 30x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '30x2'. 30x2(2 + -2x + x2) = 0 Ignore the factor 30.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 '(2 + -2x + x2)' equal to zero and attempt to solve: Simplifying 2 + -2x + x2 = 0 Solving 2 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2x + x2 = 0 + -2 -2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2x + x2 = -2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -2 + 1 Reorder the terms: 1 + -2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2x + x2 = -1 Factor a perfect square on the left side: (x + -1)(x + -1) = -1 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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