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Simplifying 4x4 + -34x2 + -28 = 0 Reorder the terms: -28 + -34x2 + 4x4 = 0 Solving -28 + -34x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + -17x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + -17x2 + 2x4)' equal to zero and attempt to solve: Simplifying -14 + -17x2 + 2x4 = 0 Solving -14 + -17x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -8.5x2 + x4 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -8.5x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + -8.5x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8.5x2 + x4 = 0 + 7 -8.5x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 -8.5x2 + x4 = 7 The x term is -8.5x2. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x2 + 18.0625 + x4 = 7 + 18.0625 Reorder the terms: 18.0625 + -8.5x2 + x4 = 7 + 18.0625 Combine like terms: 7 + 18.0625 = 25.0625 18.0625 + -8.5x2 + x4 = 25.0625 Factor a perfect square on the left side: (x2 + -4.25)(x2 + -4.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x2 + -4.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x2 + -4.25 = 5.006246099 Simplifying x2 + -4.25 = 5.006246099 Reorder the terms: -4.25 + x2 = 5.006246099 Solving -4.25 + x2 = 5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x2 = 5.006246099 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x2 = 5.006246099 + 4.25 x2 = 5.006246099 + 4.25 Combine like terms: 5.006246099 + 4.25 = 9.256246099 x2 = 9.256246099 Simplifying x2 = 9.256246099 Take the square root of each side: x = {-3.042407944, 3.042407944}Subproblem 2
x2 + -4.25 = -5.006246099 Simplifying x2 + -4.25 = -5.006246099 Reorder the terms: -4.25 + x2 = -5.006246099 Solving -4.25 + x2 = -5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x2 = -5.006246099 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x2 = -5.006246099 + 4.25 x2 = -5.006246099 + 4.25 Combine like terms: -5.006246099 + 4.25 = -0.756246099 x2 = -0.756246099 Simplifying x2 = -0.756246099 Reorder the terms: 0.756246099 + x2 = -0.756246099 + 0.756246099 Combine like terms: -0.756246099 + 0.756246099 = 0.000000000 0.756246099 + 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. 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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