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Simplifying -2x4 + 14x3 + -28x2 = 0 Reorder the terms: -28x2 + 14x3 + -2x4 = 0 Solving -28x2 + 14x3 + -2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-14 + 7x + -1x2) = 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 '(-14 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -14 + 7x + -1x2 = 0 Solving -14 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -7x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -7x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -7x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -7x + x2 = 0 + -14 -7x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -7x + x2 = -14 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -14 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -14 + 12.25 Combine like terms: -14 + 12.25 = -1.75 12.25 + -7x + x2 = -1.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -1.75 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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