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Simplifying 5x4 + -1x2 + -1 = 0 Reorder the terms: -1 + -1x2 + 5x4 = 0 Solving -1 + -1x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.2x2 + x4 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.2x2 + 0.2 + x4 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.2x2 + x4 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.2x2 + x4 = 0 + 0.2 -0.2x2 + x4 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.2x2 + x4 = 0.2 The x term is -0.2x2. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x2 + 0.01 + x4 = 0.2 + 0.01 Reorder the terms: 0.01 + -0.2x2 + x4 = 0.2 + 0.01 Combine like terms: 0.2 + 0.01 = 0.21 0.01 + -0.2x2 + x4 = 0.21 Factor a perfect square on the left side: (x2 + -0.1)(x2 + -0.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x2 + -0.1) equal to 0.458257569 and -0.458257569.Subproblem 1
x2 + -0.1 = 0.458257569 Simplifying x2 + -0.1 = 0.458257569 Reorder the terms: -0.1 + x2 = 0.458257569 Solving -0.1 + x2 = 0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x2 = 0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x2 = 0.458257569 + 0.1 x2 = 0.458257569 + 0.1 Combine like terms: 0.458257569 + 0.1 = 0.558257569 x2 = 0.558257569 Simplifying x2 = 0.558257569 Take the square root of each side: x = {-0.74716636, 0.74716636}Subproblem 2
x2 + -0.1 = -0.458257569 Simplifying x2 + -0.1 = -0.458257569 Reorder the terms: -0.1 + x2 = -0.458257569 Solving -0.1 + x2 = -0.458257569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x2 = -0.458257569 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x2 = -0.458257569 + 0.1 x2 = -0.458257569 + 0.1 Combine like terms: -0.458257569 + 0.1 = -0.358257569 x2 = -0.358257569 Simplifying x2 = -0.358257569 Reorder the terms: 0.358257569 + x2 = -0.358257569 + 0.358257569 Combine like terms: -0.358257569 + 0.358257569 = 0.000000000 0.358257569 + 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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