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Simplifying -1x4 + 34x2 + 225 = 0 Reorder the terms: 225 + 34x2 + -1x4 = 0 Solving 225 + 34x2 + -1x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + -34x2 + x4 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + -34x2 + 225 + x4 = 0 + 225 Reorder the terms: -225 + 225 + -34x2 + x4 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -34x2 + x4 = 0 + 225 -34x2 + x4 = 0 + 225 Combine like terms: 0 + 225 = 225 -34x2 + x4 = 225 The x term is -34x2. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x2 + 289 + x4 = 225 + 289 Reorder the terms: 289 + -34x2 + x4 = 225 + 289 Combine like terms: 225 + 289 = 514 289 + -34x2 + x4 = 514 Factor a perfect square on the left side: (x2 + -17)(x2 + -17) = 514 Calculate the square root of the right side: 22.671568098 Break this problem into two subproblems by setting (x2 + -17) equal to 22.671568098 and -22.671568098.Subproblem 1
x2 + -17 = 22.671568098 Simplifying x2 + -17 = 22.671568098 Reorder the terms: -17 + x2 = 22.671568098 Solving -17 + x2 = 22.671568098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x2 = 22.671568098 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = 22.671568098 + 17 x2 = 22.671568098 + 17 Combine like terms: 22.671568098 + 17 = 39.671568098 x2 = 39.671568098 Simplifying x2 = 39.671568098 Take the square root of each side: x = {-6.298536981, 6.298536981}Subproblem 2
x2 + -17 = -22.671568098 Simplifying x2 + -17 = -22.671568098 Reorder the terms: -17 + x2 = -22.671568098 Solving -17 + x2 = -22.671568098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x2 = -22.671568098 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = -22.671568098 + 17 x2 = -22.671568098 + 17 Combine like terms: -22.671568098 + 17 = -5.671568098 x2 = -5.671568098 Simplifying x2 = -5.671568098 Reorder the terms: 5.671568098 + x2 = -5.671568098 + 5.671568098 Combine like terms: -5.671568098 + 5.671568098 = 0.000000000 5.671568098 + 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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