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Simplifying x4 + -34x2 = 150 Reorder the terms: -34x2 + x4 = 150 Solving -34x2 + x4 = 150 Solving for variable 'x'. Reorder the terms: -150 + -34x2 + x4 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + -34x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + -34x2 + 150 + x4 = 0 + 150 Reorder the terms: -150 + 150 + -34x2 + x4 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -34x2 + x4 = 0 + 150 -34x2 + x4 = 0 + 150 Combine like terms: 0 + 150 = 150 -34x2 + x4 = 150 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 = 150 + 289 Reorder the terms: 289 + -34x2 + x4 = 150 + 289 Combine like terms: 150 + 289 = 439 289 + -34x2 + x4 = 439 Factor a perfect square on the left side: (x2 + -17)(x2 + -17) = 439 Calculate the square root of the right side: 20.95232684 Break this problem into two subproblems by setting (x2 + -17) equal to 20.95232684 and -20.95232684.Subproblem 1
x2 + -17 = 20.95232684 Simplifying x2 + -17 = 20.95232684 Reorder the terms: -17 + x2 = 20.95232684 Solving -17 + x2 = 20.95232684 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 = 20.95232684 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = 20.95232684 + 17 x2 = 20.95232684 + 17 Combine like terms: 20.95232684 + 17 = 37.95232684 x2 = 37.95232684 Simplifying x2 = 37.95232684 Take the square root of each side: x = {-6.160545986, 6.160545986}Subproblem 2
x2 + -17 = -20.95232684 Simplifying x2 + -17 = -20.95232684 Reorder the terms: -17 + x2 = -20.95232684 Solving -17 + x2 = -20.95232684 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 = -20.95232684 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = -20.95232684 + 17 x2 = -20.95232684 + 17 Combine like terms: -20.95232684 + 17 = -3.95232684 x2 = -3.95232684 Simplifying x2 = -3.95232684 Reorder the terms: 3.95232684 + x2 = -3.95232684 + 3.95232684 Combine like terms: -3.95232684 + 3.95232684 = 0.00000000 3.95232684 + x2 = 0.00000000 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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