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Simplifying 2x4 + -12x3 + 68x2 = 0 Reorder the terms: 68x2 + -12x3 + 2x4 = 0 Solving 68x2 + -12x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(34 + -6x + 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 '(34 + -6x + x2)' equal to zero and attempt to solve: Simplifying 34 + -6x + x2 = 0 Solving 34 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -6x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -6x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -6x + x2 = 0 + -34 -6x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -6x + x2 = -34 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -34 + 9 Reorder the terms: 9 + -6x + x2 = -34 + 9 Combine like terms: -34 + 9 = -25 9 + -6x + x2 = -25 Factor a perfect square on the left side: (x + -3)(x + -3) = -25 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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