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Simplifying 48 = x4 + -5x2 + 4 Reorder the terms: 48 = 4 + -5x2 + x4 Solving 48 = 4 + -5x2 + x4 Solving for variable 'x'. Combine like terms: 48 + -4 = 44 44 + 5x2 + -1x4 = 4 + -5x2 + x4 + -4 + 5x2 + -1x4 Reorder the terms: 44 + 5x2 + -1x4 = 4 + -4 + -5x2 + 5x2 + x4 + -1x4 Combine like terms: 4 + -4 = 0 44 + 5x2 + -1x4 = 0 + -5x2 + 5x2 + x4 + -1x4 44 + 5x2 + -1x4 = -5x2 + 5x2 + x4 + -1x4 Combine like terms: -5x2 + 5x2 = 0 44 + 5x2 + -1x4 = 0 + x4 + -1x4 44 + 5x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 44 + 5x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + -5x2 + x4 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -5x2 + 44 + x4 = 0 + 44 Reorder the terms: -44 + 44 + -5x2 + x4 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -5x2 + x4 = 0 + 44 -5x2 + x4 = 0 + 44 Combine like terms: 0 + 44 = 44 -5x2 + x4 = 44 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 44 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 44 + 6.25 Combine like terms: 44 + 6.25 = 50.25 6.25 + -5x2 + x4 = 50.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x2 + -2.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x2 + -2.5 = 7.088723439 Simplifying x2 + -2.5 = 7.088723439 Reorder the terms: -2.5 + x2 = 7.088723439 Solving -2.5 + x2 = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 7.088723439 + 2.5 x2 = 7.088723439 + 2.5 Combine like terms: 7.088723439 + 2.5 = 9.588723439 x2 = 9.588723439 Simplifying x2 = 9.588723439 Take the square root of each side: x = {-3.096566395, 3.096566395}Subproblem 2
x2 + -2.5 = -7.088723439 Simplifying x2 + -2.5 = -7.088723439 Reorder the terms: -2.5 + x2 = -7.088723439 Solving -2.5 + x2 = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -7.088723439 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -7.088723439 + 2.5 x2 = -7.088723439 + 2.5 Combine like terms: -7.088723439 + 2.5 = -4.588723439 x2 = -4.588723439 Simplifying x2 = -4.588723439 Reorder the terms: 4.588723439 + x2 = -4.588723439 + 4.588723439 Combine like terms: -4.588723439 + 4.588723439 = 0.000000000 4.588723439 + 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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