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Simplifying 16x4 + 23x3 + 126x2 = 0 Reorder the terms: 126x2 + 23x3 + 16x4 = 0 Solving 126x2 + 23x3 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(126 + 23x + 16x2) = 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 '(126 + 23x + 16x2)' equal to zero and attempt to solve: Simplifying 126 + 23x + 16x2 = 0 Solving 126 + 23x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.875 + 1.4375x + x2 = 0 Move the constant term to the right: Add '-7.875' to each side of the equation. 7.875 + 1.4375x + -7.875 + x2 = 0 + -7.875 Reorder the terms: 7.875 + -7.875 + 1.4375x + x2 = 0 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + 1.4375x + x2 = 0 + -7.875 1.4375x + x2 = 0 + -7.875 Combine like terms: 0 + -7.875 = -7.875 1.4375x + x2 = -7.875 The x term is 1.4375x. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375x + 0.5166015625 + x2 = -7.875 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = -7.875 + 0.5166015625 Combine like terms: -7.875 + 0.5166015625 = -7.3583984375 0.5166015625 + 1.4375x + x2 = -7.3583984375 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = -7.3583984375 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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