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Simplifying x(x + 1) + x + 2 = 292 Reorder the terms: x(1 + x) + x + 2 = 292 (1 * x + x * x) + x + 2 = 292 (1x + x2) + x + 2 = 292 Reorder the terms: 2 + 1x + x + x2 = 292 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 292 Solving 2 + 2x + x2 = 292 Solving for variable 'x'. Reorder the terms: 2 + -292 + 2x + x2 = 292 + -292 Combine like terms: 2 + -292 = -290 -290 + 2x + x2 = 292 + -292 Combine like terms: 292 + -292 = 0 -290 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '290' to each side of the equation. -290 + 2x + 290 + x2 = 0 + 290 Reorder the terms: -290 + 290 + 2x + x2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + 2x + x2 = 0 + 290 2x + x2 = 0 + 290 Combine like terms: 0 + 290 = 290 2x + x2 = 290 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 = 290 + 1 Reorder the terms: 1 + 2x + x2 = 290 + 1 Combine like terms: 290 + 1 = 291 1 + 2x + x2 = 291 Factor a perfect square on the left side: (x + 1)(x + 1) = 291 Calculate the square root of the right side: 17.058722109 Break this problem into two subproblems by setting (x + 1) equal to 17.058722109 and -17.058722109.Subproblem 1
x + 1 = 17.058722109 Simplifying x + 1 = 17.058722109 Reorder the terms: 1 + x = 17.058722109 Solving 1 + x = 17.058722109 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 = 17.058722109 + -1 Combine like terms: 1 + -1 = 0 0 + x = 17.058722109 + -1 x = 17.058722109 + -1 Combine like terms: 17.058722109 + -1 = 16.058722109 x = 16.058722109 Simplifying x = 16.058722109Subproblem 2
x + 1 = -17.058722109 Simplifying x + 1 = -17.058722109 Reorder the terms: 1 + x = -17.058722109 Solving 1 + x = -17.058722109 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 = -17.058722109 + -1 Combine like terms: 1 + -1 = 0 0 + x = -17.058722109 + -1 x = -17.058722109 + -1 Combine like terms: -17.058722109 + -1 = -18.058722109 x = -18.058722109 Simplifying x = -18.058722109Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.058722109, -18.058722109}
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