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Simplifying (20x3 + 8x2) + (20x3 + 10x) = 0 Reorder the terms: (8x2 + 20x3) + (20x3 + 10x) = 0 Remove parenthesis around (8x2 + 20x3) 8x2 + 20x3 + (20x3 + 10x) = 0 Reorder the terms: 8x2 + 20x3 + (10x + 20x3) = 0 Remove parenthesis around (10x + 20x3) 8x2 + 20x3 + 10x + 20x3 = 0 Reorder the terms: 10x + 8x2 + 20x3 + 20x3 = 0 Combine like terms: 20x3 + 20x3 = 40x3 10x + 8x2 + 40x3 = 0 Solving 10x + 8x2 + 40x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 4x + 20x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + 4x + 20x2)' equal to zero and attempt to solve: Simplifying 5 + 4x + 20x2 = 0 Solving 5 + 4x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.25 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.2x + -0.25 + x2 = 0.0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.2x + x2 = 0.0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.2x + x2 = 0.0 + -0.25 0.2x + x2 = 0.0 + -0.25 Combine like terms: 0.0 + -0.25 = -0.25 0.2x + x2 = -0.25 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = -0.25 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = -0.25 + 0.01 Combine like terms: -0.25 + 0.01 = -0.24 0.01 + 0.2x + x2 = -0.24 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = -0.24 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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