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Simplifying 0 = x2 + 2x + -1900 Reorder the terms: 0 = -1900 + 2x + x2 Solving 0 = -1900 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + 1900 = 1900 1900 + -2x + -1x2 = -1900 + 2x + x2 + 1900 + -2x + -1x2 Reorder the terms: 1900 + -2x + -1x2 = -1900 + 1900 + 2x + -2x + x2 + -1x2 Combine like terms: -1900 + 1900 = 0 1900 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 1900 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 1900 + -2x + -1x2 = 0 + x2 + -1x2 1900 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1900 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1900 + 2x + x2 = 0 Move the constant term to the right: Add '1900' to each side of the equation. -1900 + 2x + 1900 + x2 = 0 + 1900 Reorder the terms: -1900 + 1900 + 2x + x2 = 0 + 1900 Combine like terms: -1900 + 1900 = 0 0 + 2x + x2 = 0 + 1900 2x + x2 = 0 + 1900 Combine like terms: 0 + 1900 = 1900 2x + x2 = 1900 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 = 1900 + 1 Reorder the terms: 1 + 2x + x2 = 1900 + 1 Combine like terms: 1900 + 1 = 1901 1 + 2x + x2 = 1901 Factor a perfect square on the left side: (x + 1)(x + 1) = 1901 Calculate the square root of the right side: 43.600458713 Break this problem into two subproblems by setting (x + 1) equal to 43.600458713 and -43.600458713.Subproblem 1
x + 1 = 43.600458713 Simplifying x + 1 = 43.600458713 Reorder the terms: 1 + x = 43.600458713 Solving 1 + x = 43.600458713 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 = 43.600458713 + -1 Combine like terms: 1 + -1 = 0 0 + x = 43.600458713 + -1 x = 43.600458713 + -1 Combine like terms: 43.600458713 + -1 = 42.600458713 x = 42.600458713 Simplifying x = 42.600458713Subproblem 2
x + 1 = -43.600458713 Simplifying x + 1 = -43.600458713 Reorder the terms: 1 + x = -43.600458713 Solving 1 + x = -43.600458713 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 = -43.600458713 + -1 Combine like terms: 1 + -1 = 0 0 + x = -43.600458713 + -1 x = -43.600458713 + -1 Combine like terms: -43.600458713 + -1 = -44.600458713 x = -44.600458713 Simplifying x = -44.600458713Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.600458713, -44.600458713}
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