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Simplifying 10x4 + 60x3 + 270x2 = 0 Reorder the terms: 270x2 + 60x3 + 10x4 = 0 Solving 270x2 + 60x3 + 10x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x2'. 10x2(27 + 6x + x2) = 0 Ignore the factor 10.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 '(27 + 6x + x2)' equal to zero and attempt to solve: Simplifying 27 + 6x + x2 = 0 Solving 27 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 6x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 6x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 6x + x2 = 0 + -27 6x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 6x + x2 = -27 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -27 + 9 Reorder the terms: 9 + 6x + x2 = -27 + 9 Combine like terms: -27 + 9 = -18 9 + 6x + x2 = -18 Factor a perfect square on the left side: (x + 3)(x + 3) = -18 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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