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Simplifying 6x4 + 6x2 + -5 = 0 Reorder the terms: -5 + 6x2 + 6x4 = 0 Solving -5 + 6x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + x2 + x4 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + x2 + 0.8333333333 + x4 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + x2 + x4 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + x2 + x4 = 0 + 0.8333333333 x2 + x4 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 x2 + x4 = 0.8333333333 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. + 0.25 + x4 = 0.8333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 0.8333333333 + 0.25 Combine like terms: 0.8333333333 + 0.25 = 1.0833333333 1.25 + x4 = 1.0833333333 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 1.0833333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x2 + 0.5) equal to 1.040833 and -1.040833.Subproblem 1
x2 + 0.5 = 1.040833 Simplifying x2 + 0.5 = 1.040833 Reorder the terms: 0.5 + x2 = 1.040833 Solving 0.5 + x2 = 1.040833 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 = 1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1.040833 + -0.5 x2 = 1.040833 + -0.5 Combine like terms: 1.040833 + -0.5 = 0.540833 x2 = 0.540833 Simplifying x2 = 0.540833 Take the square root of each side: x = {-0.735413489, 0.735413489}Subproblem 2
x2 + 0.5 = -1.040833 Simplifying x2 + 0.5 = -1.040833 Reorder the terms: 0.5 + x2 = -1.040833 Solving 0.5 + x2 = -1.040833 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 = -1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1.040833 + -0.5 x2 = -1.040833 + -0.5 Combine like terms: -1.040833 + -0.5 = -1.540833 x2 = -1.540833 Simplifying x2 = -1.540833 Reorder the terms: 1.540833 + x2 = -1.540833 + 1.540833 Combine like terms: -1.540833 + 1.540833 = 0.000000 1.540833 + x2 = 0.000000 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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