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Simplifying 20x4 + -10x3 + 15x2 = 0 Reorder the terms: 15x2 + -10x3 + 20x4 = 0 Solving 15x2 + -10x3 + 20x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(3 + -2x + 4x2) = 0 Ignore the factor 5.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 '(3 + -2x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + -2x + 4x2 = 0 Solving 3 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.5x + x2 = 0 + -0.75 -0.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.5x + x2 = -0.75 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + -0.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.6875 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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