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Simplifying 16x4 + 16x3 + 28x2 = 0 Reorder the terms: 28x2 + 16x3 + 16x4 = 0 Solving 28x2 + 16x3 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(7 + 4x + 4x2) = 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 '(7 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 4x2 = 0 Solving 7 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x + x2 = 0 + -1.75 x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 x + x2 = -1.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -1.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.75 + 0.25 Combine like terms: -1.75 + 0.25 = -1.5 1.25 + x2 = -1.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.5 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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