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Simplifying 8x2 + 2x4 = 12.5 Solving 8x2 + 2x4 = 12.5 Solving for variable 'x'. Reorder the terms: -12.5 + 8x2 + 2x4 = 12.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 -12.5 + 8x2 + 2x4 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.25 + 4x2 + x4 = 0.0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 4x2 + 6.25 + x4 = 0.0 + 6.25 Reorder the terms: -6.25 + 6.25 + 4x2 + x4 = 0.0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 4x2 + x4 = 0.0 + 6.25 4x2 + x4 = 0.0 + 6.25 Combine like terms: 0.0 + 6.25 = 6.25 4x2 + x4 = 6.25 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 6.25 + 4 Reorder the terms: 4 + 4x2 + x4 = 6.25 + 4 Combine like terms: 6.25 + 4 = 10.25 4 + 4x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + 2) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + 2 = 3.201562119 Simplifying x2 + 2 = 3.201562119 Reorder the terms: 2 + x2 = 3.201562119 Solving 2 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 3.201562119 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 3.201562119 + -2 x2 = 3.201562119 + -2 Combine like terms: 3.201562119 + -2 = 1.201562119 x2 = 1.201562119 Simplifying x2 = 1.201562119 Take the square root of each side: x = {-1.09615789, 1.09615789}Subproblem 2
x2 + 2 = -3.201562119 Simplifying x2 + 2 = -3.201562119 Reorder the terms: 2 + x2 = -3.201562119 Solving 2 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -3.201562119 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -3.201562119 + -2 x2 = -3.201562119 + -2 Combine like terms: -3.201562119 + -2 = -5.201562119 x2 = -5.201562119 Simplifying x2 = -5.201562119 Reorder the terms: 5.201562119 + x2 = -5.201562119 + 5.201562119 Combine like terms: -5.201562119 + 5.201562119 = 0.000000000 5.201562119 + 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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