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Simplifying 2x4 + -144 = 73x2 Reorder the terms: -144 + 2x4 = 73x2 Solving -144 + 2x4 = 73x2 Solving for variable 'x'. Reorder the terms: -144 + -73x2 + 2x4 = 73x2 + -73x2 Combine like terms: 73x2 + -73x2 = 0 -144 + -73x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -72 + -36.5x2 + x4 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -36.5x2 + 72 + x4 = 0 + 72 Reorder the terms: -72 + 72 + -36.5x2 + x4 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -36.5x2 + x4 = 0 + 72 -36.5x2 + x4 = 0 + 72 Combine like terms: 0 + 72 = 72 -36.5x2 + x4 = 72 The x term is -36.5x2. Take half its coefficient (-18.25). Square it (333.0625) and add it to both sides. Add '333.0625' to each side of the equation. -36.5x2 + 333.0625 + x4 = 72 + 333.0625 Reorder the terms: 333.0625 + -36.5x2 + x4 = 72 + 333.0625 Combine like terms: 72 + 333.0625 = 405.0625 333.0625 + -36.5x2 + x4 = 405.0625 Factor a perfect square on the left side: (x2 + -18.25)(x2 + -18.25) = 405.0625 Calculate the square root of the right side: 20.126164563 Break this problem into two subproblems by setting (x2 + -18.25) equal to 20.126164563 and -20.126164563.Subproblem 1
x2 + -18.25 = 20.126164563 Simplifying x2 + -18.25 = 20.126164563 Reorder the terms: -18.25 + x2 = 20.126164563 Solving -18.25 + x2 = 20.126164563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.25' to each side of the equation. -18.25 + 18.25 + x2 = 20.126164563 + 18.25 Combine like terms: -18.25 + 18.25 = 0.00 0.00 + x2 = 20.126164563 + 18.25 x2 = 20.126164563 + 18.25 Combine like terms: 20.126164563 + 18.25 = 38.376164563 x2 = 38.376164563 Simplifying x2 = 38.376164563 Take the square root of each side: x = {-6.194849842, 6.194849842}Subproblem 2
x2 + -18.25 = -20.126164563 Simplifying x2 + -18.25 = -20.126164563 Reorder the terms: -18.25 + x2 = -20.126164563 Solving -18.25 + x2 = -20.126164563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.25' to each side of the equation. -18.25 + 18.25 + x2 = -20.126164563 + 18.25 Combine like terms: -18.25 + 18.25 = 0.00 0.00 + x2 = -20.126164563 + 18.25 x2 = -20.126164563 + 18.25 Combine like terms: -20.126164563 + 18.25 = -1.876164563 x2 = -1.876164563 Simplifying x2 = -1.876164563 Reorder the terms: 1.876164563 + x2 = -1.876164563 + 1.876164563 Combine like terms: -1.876164563 + 1.876164563 = 0.000000000 1.876164563 + 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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