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Simplifying 8x4 + -25x3 + 21x2 = 0 Reorder the terms: 21x2 + -25x3 + 8x4 = 0 Solving 21x2 + -25x3 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(21 + -25x + 8x2) = 0Subproblem 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 '(21 + -25x + 8x2)' equal to zero and attempt to solve: Simplifying 21 + -25x + 8x2 = 0 Solving 21 + -25x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.625 + -3.125x + x2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + -3.125x + -2.625 + x2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + -3.125x + x2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + -3.125x + x2 = 0 + -2.625 -3.125x + x2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 -3.125x + x2 = -2.625 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = -2.625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = -2.625 + 2.44140625 Combine like terms: -2.625 + 2.44140625 = -0.18359375 2.44140625 + -3.125x + x2 = -0.18359375 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = -0.18359375 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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