8x^4-12x^3+20x^2=

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Solution for 8x^4-12x^3+20x^2= equation:


Simplifying
8x4 + -12x3 + 20x2 = 0

Reorder the terms:
20x2 + -12x3 + 8x4 = 0

Solving
20x2 + -12x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(5 + -3x + 2x2) = 0

Ignore the factor 4.

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 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -3x + 2x2 = 0 Solving 5 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5x + x2 = 0 + -2.5 -1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5x + x2 = -2.5 The x term is -1.5x. 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. -1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.9375 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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