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Simplifying 8x4 + 10x2 + -11 = 0 Reorder the terms: -11 + 10x2 + 8x4 = 0 Solving -11 + 10x2 + 8x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 1.25x2 + x4 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 1.25x2 + 1.375 + x4 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 1.25x2 + x4 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 1.25x2 + x4 = 0 + 1.375 1.25x2 + x4 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 1.25x2 + x4 = 1.375 The x term is 1.25x2. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x2 + 0.390625 + x4 = 1.375 + 0.390625 Reorder the terms: 0.390625 + 1.25x2 + x4 = 1.375 + 0.390625 Combine like terms: 1.375 + 0.390625 = 1.765625 0.390625 + 1.25x2 + x4 = 1.765625 Factor a perfect square on the left side: (x2 + 0.625)(x2 + 0.625) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x2 + 0.625) equal to 1.328768227 and -1.328768227.Subproblem 1
x2 + 0.625 = 1.328768227 Simplifying x2 + 0.625 = 1.328768227 Reorder the terms: 0.625 + x2 = 1.328768227 Solving 0.625 + x2 = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x2 = 1.328768227 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x2 = 1.328768227 + -0.625 x2 = 1.328768227 + -0.625 Combine like terms: 1.328768227 + -0.625 = 0.703768227 x2 = 0.703768227 Simplifying x2 = 0.703768227 Take the square root of each side: x = {-0.83890895, 0.83890895}Subproblem 2
x2 + 0.625 = -1.328768227 Simplifying x2 + 0.625 = -1.328768227 Reorder the terms: 0.625 + x2 = -1.328768227 Solving 0.625 + x2 = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x2 = -1.328768227 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x2 = -1.328768227 + -0.625 x2 = -1.328768227 + -0.625 Combine like terms: -1.328768227 + -0.625 = -1.953768227 x2 = -1.953768227 Simplifying x2 = -1.953768227 Reorder the terms: 1.953768227 + x2 = -1.953768227 + 1.953768227 Combine like terms: -1.953768227 + 1.953768227 = 0.000000000 1.953768227 + 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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