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Simplifying 2x4 = 2x3 + -24x2 Reorder the terms: 2x4 = -24x2 + 2x3 Solving 2x4 = -24x2 + 2x3 Solving for variable 'x'. Reorder the terms: 24x2 + -2x3 + 2x4 = -24x2 + 2x3 + 24x2 + -2x3 Reorder the terms: 24x2 + -2x3 + 2x4 = -24x2 + 24x2 + 2x3 + -2x3 Combine like terms: -24x2 + 24x2 = 0 24x2 + -2x3 + 2x4 = 0 + 2x3 + -2x3 24x2 + -2x3 + 2x4 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 24x2 + -2x3 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(12 + -1x + x2) = 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 '(12 + -1x + x2)' equal to zero and attempt to solve: Simplifying 12 + -1x + x2 = 0 Solving 12 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -1x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -1x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x + x2 = 0 + -12 -1x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1x + x2 = -12 The x term is -1x. 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. -1x + 0.25 + x2 = -12 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + -1x + x2 = -11.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -11.75 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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