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Simplifying 28x4 + 20x3 + 4x2 = 0 Reorder the terms: 4x2 + 20x3 + 28x4 = 0 Solving 4x2 + 20x3 + 28x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(1 + 5x + 7x2) = 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 '(1 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 5x + 7x2 = 0 Solving 1 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.7142857143x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.7142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + -0.1428571429 0.7142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.7142857143x + x2 = -0.1428571429 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -0.1428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -0.1428571429 + 0.1275510204 Combine like terms: -0.1428571429 + 0.1275510204 = -0.0153061225 0.1275510204 + 0.7142857143x + x2 = -0.0153061225 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = -0.0153061225 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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