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Simplifying 26x4 + 4x2 + -1 = 0 Reorder the terms: -1 + 4x2 + 26x4 = 0 Solving -1 + 4x2 + 26x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.03846153846 + 0.1538461538x2 + x4 = 0 Move the constant term to the right: Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.1538461538x2 + 0.03846153846 + x4 = 0 + 0.03846153846 Reorder the terms: -0.03846153846 + 0.03846153846 + 0.1538461538x2 + x4 = 0 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + 0.1538461538x2 + x4 = 0 + 0.03846153846 0.1538461538x2 + x4 = 0 + 0.03846153846 Combine like terms: 0 + 0.03846153846 = 0.03846153846 0.1538461538x2 + x4 = 0.03846153846 The x term is 0.1538461538x2. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x2 + 0.005917159760 + x4 = 0.03846153846 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x2 + x4 = 0.03846153846 + 0.005917159760 Combine like terms: 0.03846153846 + 0.005917159760 = 0.04437869822 0.005917159760 + 0.1538461538x2 + x4 = 0.04437869822 Factor a perfect square on the left side: (x2 + 0.0769230769)(x2 + 0.0769230769) = 0.04437869822 Calculate the square root of the right side: 0.210662522 Break this problem into two subproblems by setting (x2 + 0.0769230769) equal to 0.210662522 and -0.210662522.Subproblem 1
x2 + 0.0769230769 = 0.210662522 Simplifying x2 + 0.0769230769 = 0.210662522 Reorder the terms: 0.0769230769 + x2 = 0.210662522 Solving 0.0769230769 + x2 = 0.210662522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x2 = 0.210662522 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x2 = 0.210662522 + -0.0769230769 x2 = 0.210662522 + -0.0769230769 Combine like terms: 0.210662522 + -0.0769230769 = 0.1337394451 x2 = 0.1337394451 Simplifying x2 = 0.1337394451 Take the square root of each side: x = {-0.36570404, 0.36570404}Subproblem 2
x2 + 0.0769230769 = -0.210662522 Simplifying x2 + 0.0769230769 = -0.210662522 Reorder the terms: 0.0769230769 + x2 = -0.210662522 Solving 0.0769230769 + x2 = -0.210662522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x2 = -0.210662522 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x2 = -0.210662522 + -0.0769230769 x2 = -0.210662522 + -0.0769230769 Combine like terms: -0.210662522 + -0.0769230769 = -0.2875855989 x2 = -0.2875855989 Simplifying x2 = -0.2875855989 Reorder the terms: 0.2875855989 + x2 = -0.2875855989 + 0.2875855989 Combine like terms: -0.2875855989 + 0.2875855989 = 0.0000000000 0.2875855989 + x2 = 0.0000000000 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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