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Simplifying (-1x4) + (8x2) + -2 = 0 Reorder the terms: -2 + (8x2) + (-1x4) = 0 Solving -2 + (8x2) + (-1x4) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + (-8x2) + x4 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + (-8x2) + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + (-8x2) + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + (-8x2) + x4 = 0 + -2 (-8x2) + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 (-8x2) + x4 = -2 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 = -2 + 16 Reorder the terms: 16 + (-8x2) + x4 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + (-8x2) + x4 = 14 Factor a perfect square on the left side: ((x2) + -4)((x2) + -4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting ((x2) + -4) equal to 3.741657387 and -3.741657387.Subproblem 1
(x2) + -4 = 3.741657387 Simplifying (x2) + -4 = 3.741657387 x2 + -4 = 3.741657387 Reorder the terms: -4 + x2 = 3.741657387 Solving -4 + x2 = 3.741657387 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 = 3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.741657387 + 4 x2 = 3.741657387 + 4 Combine like terms: 3.741657387 + 4 = 7.741657387 x2 = 7.741657387 Simplifying x2 = 7.741657387 Take the square root of each side: x = {-2.7823834, 2.7823834}Subproblem 2
(x2) + -4 = -3.741657387 Simplifying (x2) + -4 = -3.741657387 x2 + -4 = -3.741657387 Reorder the terms: -4 + x2 = -3.741657387 Solving -4 + x2 = -3.741657387 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 = -3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.741657387 + 4 x2 = -3.741657387 + 4 Combine like terms: -3.741657387 + 4 = 0.258342613 x2 = 0.258342613 Simplifying x2 = 0.258342613 Take the square root of each side: x = {-0.508274151, 0.508274151}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.7823834, 2.7823834, -0.508274151, 0.508274151}
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