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Simplifying 2x4 + x2 = 49 Reorder the terms: x2 + 2x4 = 49 Solving x2 + 2x4 = 49 Solving for variable 'x'. Reorder the terms: -49 + x2 + 2x4 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + 0.5x2 + 24.5 + x4 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + 0.5x2 + x4 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + 0.5x2 + x4 = 0 + 24.5 0.5x2 + x4 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 0.5x2 + x4 = 24.5 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 = 24.5 + 0.25 Reorder the terms: 0.25 + 0.5x2 + x4 = 24.5 + 0.25 Combine like terms: 24.5 + 0.25 = 24.75 0.25 + 0.5x2 + x4 = 24.75 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x2 + 0.5) equal to 4.974937186 and -4.974937186.Subproblem 1
x2 + 0.5 = 4.974937186 Simplifying x2 + 0.5 = 4.974937186 Reorder the terms: 0.5 + x2 = 4.974937186 Solving 0.5 + x2 = 4.974937186 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 = 4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 4.974937186 + -0.5 x2 = 4.974937186 + -0.5 Combine like terms: 4.974937186 + -0.5 = 4.474937186 x2 = 4.474937186 Simplifying x2 = 4.474937186 Take the square root of each side: x = {-2.115404733, 2.115404733}Subproblem 2
x2 + 0.5 = -4.974937186 Simplifying x2 + 0.5 = -4.974937186 Reorder the terms: 0.5 + x2 = -4.974937186 Solving 0.5 + x2 = -4.974937186 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 = -4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -4.974937186 + -0.5 x2 = -4.974937186 + -0.5 Combine like terms: -4.974937186 + -0.5 = -5.474937186 x2 = -5.474937186 Simplifying x2 = -5.474937186 Reorder the terms: 5.474937186 + x2 = -5.474937186 + 5.474937186 Combine like terms: -5.474937186 + 5.474937186 = 0.000000000 5.474937186 + 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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