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Simplifying 2x2 + 4x + -165 = 0 Reorder the terms: -165 + 4x + 2x2 = 0 Solving -165 + 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'. -82.5 + 2x + x2 = 0 Move the constant term to the right: Add '82.5' to each side of the equation. -82.5 + 2x + 82.5 + x2 = 0 + 82.5 Reorder the terms: -82.5 + 82.5 + 2x + x2 = 0 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + 2x + x2 = 0 + 82.5 2x + x2 = 0 + 82.5 Combine like terms: 0 + 82.5 = 82.5 2x + x2 = 82.5 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 = 82.5 + 1 Reorder the terms: 1 + 2x + x2 = 82.5 + 1 Combine like terms: 82.5 + 1 = 83.5 1 + 2x + x2 = 83.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 83.5 Calculate the square root of the right side: 9.137833441 Break this problem into two subproblems by setting (x + 1) equal to 9.137833441 and -9.137833441.Subproblem 1
x + 1 = 9.137833441 Simplifying x + 1 = 9.137833441 Reorder the terms: 1 + x = 9.137833441 Solving 1 + x = 9.137833441 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 = 9.137833441 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.137833441 + -1 x = 9.137833441 + -1 Combine like terms: 9.137833441 + -1 = 8.137833441 x = 8.137833441 Simplifying x = 8.137833441Subproblem 2
x + 1 = -9.137833441 Simplifying x + 1 = -9.137833441 Reorder the terms: 1 + x = -9.137833441 Solving 1 + x = -9.137833441 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 = -9.137833441 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.137833441 + -1 x = -9.137833441 + -1 Combine like terms: -9.137833441 + -1 = -10.137833441 x = -10.137833441 Simplifying x = -10.137833441Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.137833441, -10.137833441}
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