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Simplifying 0 = (0.25x4) + -1(2x2) + -1 Remove parenthesis around (2x2) 0 = (0.25x4) + -1 * 2x2 + -1 Multiply -1 * 2 0 = (0.25x4) + -2x2 + -1 Reorder the terms: 0 = -1 + -2x2 + (0.25x4) Solving 0 = -1 + -2x2 + (0.25x4) Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + 2x2 + (-0.25x4) = -1 + -2x2 + (0.25x4) + 1 + 2x2 + (-0.25x4) Reorder the terms: 1 + 2x2 + (-0.25x4) = -1 + 1 + -2x2 + 2x2 + (0.25x4) + (-0.25x4) Combine like terms: -1 + 1 = 0 1 + 2x2 + (-0.25x4) = 0 + -2x2 + 2x2 + (0.25x4) + (-0.25x4) 1 + 2x2 + (-0.25x4) = -2x2 + 2x2 + (0.25x4) + (-0.25x4) Combine like terms: -2x2 + 2x2 = 0 1 + 2x2 + (-0.25x4) = 0 + (0.25x4) + (-0.25x4) 1 + 2x2 + (-0.25x4) = (0.25x4) + (-0.25x4) Combine like terms: (0.25x4) + (-0.25x4) = 0.00 1 + 2x2 + (-0.25x4) = 0.00 Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -4 + -8x2 + x4 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -8x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8x2 + x4 = 0 + 4 -8x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -8x2 + x4 = 4 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 4 + 16 Reorder the terms: 16 + -8x2 + x4 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8x2 + x4 = 20 Factor a perfect square on the left side: ((x2) + -4)((x2) + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting ((x2) + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
(x2) + -4 = 4.472135955 Simplifying (x2) + -4 = 4.472135955 x2 + -4 = 4.472135955 Reorder the terms: -4 + x2 = 4.472135955 Solving -4 + x2 = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 4.472135955 + 4 x2 = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 x2 = 8.472135955 Simplifying x2 = 8.472135955 Take the square root of each side: x = {-2.91069338, 2.91069338}Subproblem 2
(x2) + -4 = -4.472135955 Simplifying (x2) + -4 = -4.472135955 x2 + -4 = -4.472135955 Reorder the terms: -4 + x2 = -4.472135955 Solving -4 + x2 = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -4.472135955 + 4 x2 = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 x2 = -0.472135955 Simplifying x2 = -0.472135955 Reorder the terms: 0.472135955 + x2 = -0.472135955 + 0.472135955 Combine like terms: -0.472135955 + 0.472135955 = 0.000000000 0.472135955 + 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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