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Simplifying 1805 = x2 + 2x Reorder the terms: 1805 = 2x + x2 Solving 1805 = 2x + x2 Solving for variable 'x'. Reorder the terms: 1805 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 1805 + -2x + -1x2 = 0 + x2 + -1x2 1805 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1805 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1805 + 2x + x2 = 0 Move the constant term to the right: Add '1805' to each side of the equation. -1805 + 2x + 1805 + x2 = 0 + 1805 Reorder the terms: -1805 + 1805 + 2x + x2 = 0 + 1805 Combine like terms: -1805 + 1805 = 0 0 + 2x + x2 = 0 + 1805 2x + x2 = 0 + 1805 Combine like terms: 0 + 1805 = 1805 2x + x2 = 1805 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 = 1805 + 1 Reorder the terms: 1 + 2x + x2 = 1805 + 1 Combine like terms: 1805 + 1 = 1806 1 + 2x + x2 = 1806 Factor a perfect square on the left side: (x + 1)(x + 1) = 1806 Calculate the square root of the right side: 42.497058722 Break this problem into two subproblems by setting (x + 1) equal to 42.497058722 and -42.497058722.Subproblem 1
x + 1 = 42.497058722 Simplifying x + 1 = 42.497058722 Reorder the terms: 1 + x = 42.497058722 Solving 1 + x = 42.497058722 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 = 42.497058722 + -1 Combine like terms: 1 + -1 = 0 0 + x = 42.497058722 + -1 x = 42.497058722 + -1 Combine like terms: 42.497058722 + -1 = 41.497058722 x = 41.497058722 Simplifying x = 41.497058722Subproblem 2
x + 1 = -42.497058722 Simplifying x + 1 = -42.497058722 Reorder the terms: 1 + x = -42.497058722 Solving 1 + x = -42.497058722 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 = -42.497058722 + -1 Combine like terms: 1 + -1 = 0 0 + x = -42.497058722 + -1 x = -42.497058722 + -1 Combine like terms: -42.497058722 + -1 = -43.497058722 x = -43.497058722 Simplifying x = -43.497058722Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.497058722, -43.497058722}
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