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Simplifying 2x2 + 4x + -177 = 0 Reorder the terms: -177 + 4x + 2x2 = 0 Solving -177 + 4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -88.5 + 2x + x2 = 0 Move the constant term to the right: Add '88.5' to each side of the equation. -88.5 + 2x + 88.5 + x2 = 0 + 88.5 Reorder the terms: -88.5 + 88.5 + 2x + x2 = 0 + 88.5 Combine like terms: -88.5 + 88.5 = 0.0 0.0 + 2x + x2 = 0 + 88.5 2x + x2 = 0 + 88.5 Combine like terms: 0 + 88.5 = 88.5 2x + x2 = 88.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 88.5 + 1 Reorder the terms: 1 + 2x + x2 = 88.5 + 1 Combine like terms: 88.5 + 1 = 89.5 1 + 2x + x2 = 89.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 89.5 Calculate the square root of the right side: 9.460443964 Break this problem into two subproblems by setting (x + 1) equal to 9.460443964 and -9.460443964.Subproblem 1
x + 1 = 9.460443964 Simplifying x + 1 = 9.460443964 Reorder the terms: 1 + x = 9.460443964 Solving 1 + x = 9.460443964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.460443964 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.460443964 + -1 x = 9.460443964 + -1 Combine like terms: 9.460443964 + -1 = 8.460443964 x = 8.460443964 Simplifying x = 8.460443964Subproblem 2
x + 1 = -9.460443964 Simplifying x + 1 = -9.460443964 Reorder the terms: 1 + x = -9.460443964 Solving 1 + x = -9.460443964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.460443964 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.460443964 + -1 x = -9.460443964 + -1 Combine like terms: -9.460443964 + -1 = -10.460443964 x = -10.460443964 Simplifying x = -10.460443964Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.460443964, -10.460443964}
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