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Simplifying 9x4 + x2 + -100 = 0 Reorder the terms: -100 + x2 + 9x4 = 0 Solving -100 + x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -11.11111111 + 0.1111111111x2 + x4 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + 0.1111111111x2 + 11.11111111 + x4 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + 0.1111111111x2 + x4 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + 0.1111111111x2 + x4 = 0 + 11.11111111 0.1111111111x2 + x4 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 0.1111111111x2 + x4 = 11.11111111 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x2 + 0.25 + x4 = 11.11111111 + 0.25 Reorder the terms: 0.25 + 0.1111111111x2 + x4 = 11.11111111 + 0.25 Combine like terms: 11.11111111 + 0.25 = 11.36111111 0.25 + 0.1111111111x2 + x4 = 11.36111111 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 11.36111111 Calculate the square root of the right side: 3.370624736 Break this problem into two subproblems by setting (x2 + 0.5) equal to 3.370624736 and -3.370624736.Subproblem 1
x2 + 0.5 = 3.370624736 Simplifying x2 + 0.5 = 3.370624736 Reorder the terms: 0.5 + x2 = 3.370624736 Solving 0.5 + x2 = 3.370624736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 3.370624736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 3.370624736 + -0.5 x2 = 3.370624736 + -0.5 Combine like terms: 3.370624736 + -0.5 = 2.870624736 x2 = 2.870624736 Simplifying x2 = 2.870624736 Take the square root of each side: x = {-1.69429181, 1.69429181}Subproblem 2
x2 + 0.5 = -3.370624736 Simplifying x2 + 0.5 = -3.370624736 Reorder the terms: 0.5 + x2 = -3.370624736 Solving 0.5 + x2 = -3.370624736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -3.370624736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -3.370624736 + -0.5 x2 = -3.370624736 + -0.5 Combine like terms: -3.370624736 + -0.5 = -3.870624736 x2 = -3.870624736 Simplifying x2 = -3.870624736 Reorder the terms: 3.870624736 + x2 = -3.870624736 + 3.870624736 Combine like terms: -3.870624736 + 3.870624736 = 0.000000000 3.870624736 + 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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