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Simplifying 3x4 + -3x2 + -14 = 0 Reorder the terms: -14 + -3x2 + 3x4 = 0 Solving -14 + -3x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -1x2 + x4 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -1x2 + 4.666666667 + x4 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -1x2 + x4 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -1x2 + x4 = 0 + 4.666666667 -1x2 + x4 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -1x2 + x4 = 4.666666667 The x term is -1x2. 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. -1x2 + 0.25 + x4 = 4.666666667 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 4.666666667 + 0.25 Combine like terms: 4.666666667 + 0.25 = 4.916666667 0.25 + -1x2 + x4 = 4.916666667 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (x2 + -0.5) equal to 2.217355783 and -2.217355783.Subproblem 1
x2 + -0.5 = 2.217355783 Simplifying x2 + -0.5 = 2.217355783 Reorder the terms: -0.5 + x2 = 2.217355783 Solving -0.5 + x2 = 2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 2.217355783 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 2.217355783 + 0.5 x2 = 2.217355783 + 0.5 Combine like terms: 2.217355783 + 0.5 = 2.717355783 x2 = 2.717355783 Simplifying x2 = 2.717355783 Take the square root of each side: x = {-1.648440409, 1.648440409}Subproblem 2
x2 + -0.5 = -2.217355783 Simplifying x2 + -0.5 = -2.217355783 Reorder the terms: -0.5 + x2 = -2.217355783 Solving -0.5 + x2 = -2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -2.217355783 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -2.217355783 + 0.5 x2 = -2.217355783 + 0.5 Combine like terms: -2.217355783 + 0.5 = -1.717355783 x2 = -1.717355783 Simplifying x2 = -1.717355783 Reorder the terms: 1.717355783 + x2 = -1.717355783 + 1.717355783 Combine like terms: -1.717355783 + 1.717355783 = 0.000000000 1.717355783 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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