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Simplifying 2x4 + x2 = 32 Reorder the terms: x2 + 2x4 = 32 Solving x2 + 2x4 = 32 Solving for variable 'x'. Reorder the terms: -32 + x2 + 2x4 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 0.5x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 0.5x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 0.5x2 + x4 = 0 + 16 0.5x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 0.5x2 + x4 = 16 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. 0.5x2 + 0.25 + x4 = 16 + 0.25 Reorder the terms: 0.25 + 0.5x2 + x4 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + 0.5x2 + x4 = 16.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x2 + 0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x2 + 0.5 = 4.031128874 Simplifying x2 + 0.5 = 4.031128874 Reorder the terms: 0.5 + x2 = 4.031128874 Solving 0.5 + x2 = 4.031128874 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 = 4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 4.031128874 + -0.5 x2 = 4.031128874 + -0.5 Combine like terms: 4.031128874 + -0.5 = 3.531128874 x2 = 3.531128874 Simplifying x2 = 3.531128874 Take the square root of each side: x = {-1.879129818, 1.879129818}Subproblem 2
x2 + 0.5 = -4.031128874 Simplifying x2 + 0.5 = -4.031128874 Reorder the terms: 0.5 + x2 = -4.031128874 Solving 0.5 + x2 = -4.031128874 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 = -4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -4.031128874 + -0.5 x2 = -4.031128874 + -0.5 Combine like terms: -4.031128874 + -0.5 = -4.531128874 x2 = -4.531128874 Simplifying x2 = -4.531128874 Reorder the terms: 4.531128874 + x2 = -4.531128874 + 4.531128874 Combine like terms: -4.531128874 + 4.531128874 = 0.000000000 4.531128874 + 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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