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Simplifying 0.125x4 + 2.5x2 + -3 = 0 Reorder the terms: -3 + 2.5x2 + 0.125x4 = 0 Solving -3 + 2.5x2 + 0.125x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. -24 + 20x2 + x4 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 20x2 + 24 + x4 = 0 + 24 Reorder the terms: -24 + 24 + 20x2 + x4 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 20x2 + x4 = 0 + 24 20x2 + x4 = 0 + 24 Combine like terms: 0 + 24 = 24 20x2 + x4 = 24 The x term is 20x2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x2 + 100 + x4 = 24 + 100 Reorder the terms: 100 + 20x2 + x4 = 24 + 100 Combine like terms: 24 + 100 = 124 100 + 20x2 + x4 = 124 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x2 + 10) equal to 11.135528726 and -11.135528726.Subproblem 1
x2 + 10 = 11.135528726 Simplifying x2 + 10 = 11.135528726 Reorder the terms: 10 + x2 = 11.135528726 Solving 10 + x2 = 11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = 11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = 11.135528726 + -10 x2 = 11.135528726 + -10 Combine like terms: 11.135528726 + -10 = 1.135528726 x2 = 1.135528726 Simplifying x2 = 1.135528726 Take the square root of each side: x = {-1.065611902, 1.065611902}Subproblem 2
x2 + 10 = -11.135528726 Simplifying x2 + 10 = -11.135528726 Reorder the terms: 10 + x2 = -11.135528726 Solving 10 + x2 = -11.135528726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = -11.135528726 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = -11.135528726 + -10 x2 = -11.135528726 + -10 Combine like terms: -11.135528726 + -10 = -21.135528726 x2 = -21.135528726 Simplifying x2 = -21.135528726 Reorder the terms: 21.135528726 + x2 = -21.135528726 + 21.135528726 Combine like terms: -21.135528726 + 21.135528726 = 0.000000000 21.135528726 + 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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