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Simplifying 9x4 + -25x2 = 16 Reorder the terms: -25x2 + 9x4 = 16 Solving -25x2 + 9x4 = 16 Solving for variable 'x'. Reorder the terms: -16 + -25x2 + 9x4 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -25x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -2.777777778x2 + x4 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -2.777777778x2 + 1.777777778 + x4 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -2.777777778x2 + x4 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -2.777777778x2 + x4 = 0 + 1.777777778 -2.777777778x2 + x4 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -2.777777778x2 + x4 = 1.777777778 The x term is -2.777777778x2. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778x2 + 1.929012346 + x4 = 1.777777778 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x2 + x4 = 1.777777778 + 1.929012346 Combine like terms: 1.777777778 + 1.929012346 = 3.706790124 1.929012346 + -2.777777778x2 + x4 = 3.706790124 Factor a perfect square on the left side: (x2 + -1.388888889)(x2 + -1.388888889) = 3.706790124 Calculate the square root of the right side: 1.925302606 Break this problem into two subproblems by setting (x2 + -1.388888889) equal to 1.925302606 and -1.925302606.Subproblem 1
x2 + -1.388888889 = 1.925302606 Simplifying x2 + -1.388888889 = 1.925302606 Reorder the terms: -1.388888889 + x2 = 1.925302606 Solving -1.388888889 + x2 = 1.925302606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x2 = 1.925302606 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x2 = 1.925302606 + 1.388888889 x2 = 1.925302606 + 1.388888889 Combine like terms: 1.925302606 + 1.388888889 = 3.314191495 x2 = 3.314191495 Simplifying x2 = 3.314191495 Take the square root of each side: x = {-1.820492102, 1.820492102}Subproblem 2
x2 + -1.388888889 = -1.925302606 Simplifying x2 + -1.388888889 = -1.925302606 Reorder the terms: -1.388888889 + x2 = -1.925302606 Solving -1.388888889 + x2 = -1.925302606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x2 = -1.925302606 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x2 = -1.925302606 + 1.388888889 x2 = -1.925302606 + 1.388888889 Combine like terms: -1.925302606 + 1.388888889 = -0.536413717 x2 = -0.536413717 Simplifying x2 = -0.536413717 Reorder the terms: 0.536413717 + x2 = -0.536413717 + 0.536413717 Combine like terms: -0.536413717 + 0.536413717 = 0.000000000 0.536413717 + 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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