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Simplifying (x2 + -4x + 2) + -96 = 0 Reorder the terms: (2 + -4x + x2) + -96 = 0 Remove parenthesis around (2 + -4x + x2) 2 + -4x + x2 + -96 = 0 Reorder the terms: 2 + -96 + -4x + x2 = 0 Combine like terms: 2 + -96 = -94 -94 + -4x + x2 = 0 Solving -94 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + -4x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + -4x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + -4x + x2 = 0 + 94 -4x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 -4x + x2 = 94 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 94 + 4 Reorder the terms: 4 + -4x + x2 = 94 + 4 Combine like terms: 94 + 4 = 98 4 + -4x + x2 = 98 Factor a perfect square on the left side: (x + -2)(x + -2) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -2) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -2 = 9.899494937 Simplifying x + -2 = 9.899494937 Reorder the terms: -2 + x = 9.899494937 Solving -2 + x = 9.899494937 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 + x = 9.899494937 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.899494937 + 2 x = 9.899494937 + 2 Combine like terms: 9.899494937 + 2 = 11.899494937 x = 11.899494937 Simplifying x = 11.899494937Subproblem 2
x + -2 = -9.899494937 Simplifying x + -2 = -9.899494937 Reorder the terms: -2 + x = -9.899494937 Solving -2 + x = -9.899494937 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 + x = -9.899494937 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.899494937 + 2 x = -9.899494937 + 2 Combine like terms: -9.899494937 + 2 = -7.899494937 x = -7.899494937 Simplifying x = -7.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.899494937, -7.899494937}
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