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Simplifying 5x4 + 3x2 + -6 = 0 Reorder the terms: -6 + 3x2 + 5x4 = 0 Solving -6 + 3x2 + 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'. -1.2 + 0.6x2 + x4 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.6x2 + 1.2 + x4 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.6x2 + x4 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.6x2 + x4 = 0 + 1.2 0.6x2 + x4 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.6x2 + x4 = 1.2 The x term is 0.6x2. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x2 + 0.09 + x4 = 1.2 + 0.09 Reorder the terms: 0.09 + 0.6x2 + x4 = 1.2 + 0.09 Combine like terms: 1.2 + 0.09 = 1.29 0.09 + 0.6x2 + x4 = 1.29 Factor a perfect square on the left side: (x2 + 0.3)(x2 + 0.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x2 + 0.3) equal to 1.135781669 and -1.135781669.Subproblem 1
x2 + 0.3 = 1.135781669 Simplifying x2 + 0.3 = 1.135781669 Reorder the terms: 0.3 + x2 = 1.135781669 Solving 0.3 + x2 = 1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x2 = 1.135781669 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x2 = 1.135781669 + -0.3 x2 = 1.135781669 + -0.3 Combine like terms: 1.135781669 + -0.3 = 0.835781669 x2 = 0.835781669 Simplifying x2 = 0.835781669 Take the square root of each side: x = {-0.914210954, 0.914210954}Subproblem 2
x2 + 0.3 = -1.135781669 Simplifying x2 + 0.3 = -1.135781669 Reorder the terms: 0.3 + x2 = -1.135781669 Solving 0.3 + x2 = -1.135781669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x2 = -1.135781669 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x2 = -1.135781669 + -0.3 x2 = -1.135781669 + -0.3 Combine like terms: -1.135781669 + -0.3 = -1.435781669 x2 = -1.435781669 Simplifying x2 = -1.435781669 Reorder the terms: 1.435781669 + x2 = -1.435781669 + 1.435781669 Combine like terms: -1.435781669 + 1.435781669 = 0.000000000 1.435781669 + 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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