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Simplifying x2 + -2x = 1900 Reorder the terms: -2x + x2 = 1900 Solving -2x + x2 = 1900 Solving for variable 'x'. Reorder the terms: -1900 + -2x + x2 = 1900 + -1900 Combine like terms: 1900 + -1900 = 0 -1900 + -2x + x2 = 0 Begin completing the square. 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 = 44.600458713 x = 44.600458713 Simplifying x = 44.600458713Subproblem 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 = -42.600458713 x = -42.600458713 Simplifying x = -42.600458713Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.600458713, -42.600458713}
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