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Simplifying 14x4 + -4x3 + 8x2 = 0 Reorder the terms: 8x2 + -4x3 + 14x4 = 0 Solving 8x2 + -4x3 + 14x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(4 + -2x + 7x2) = 0 Ignore the factor 2.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 '(4 + -2x + 7x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + 7x2 = 0 Solving 4 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -0.2857142857x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -0.2857142857x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + -0.5714285714 -0.2857142857x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -0.2857142857x + x2 = -0.5714285714 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = -0.5714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = -0.5714285714 + 0.02040816328 Combine like terms: -0.5714285714 + 0.02040816328 = -0.55102040812 0.02040816328 + -0.2857142857x + x2 = -0.55102040812 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = -0.55102040812 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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