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Simplifying (x2) + 2x = (660000) * 2 x2 + 2x = (660000) * 2 Reorder the terms: 2x + x2 = (660000) * 2 Multiply 660000 * 2 2x + x2 = 1320000 Solving 2x + x2 = 1320000 Solving for variable 'x'. Reorder the terms: -1320000 + 2x + x2 = 1320000 + -1320000 Combine like terms: 1320000 + -1320000 = 0 -1320000 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1320000' to each side of the equation. -1320000 + 2x + 1320000 + x2 = 0 + 1320000 Reorder the terms: -1320000 + 1320000 + 2x + x2 = 0 + 1320000 Combine like terms: -1320000 + 1320000 = 0 0 + 2x + x2 = 0 + 1320000 2x + x2 = 0 + 1320000 Combine like terms: 0 + 1320000 = 1320000 2x + x2 = 1320000 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 = 1320000 + 1 Reorder the terms: 1 + 2x + x2 = 1320000 + 1 Combine like terms: 1320000 + 1 = 1320001 1 + 2x + x2 = 1320001 Factor a perfect square on the left side: (x + 1)(x + 1) = 1320001 Calculate the square root of the right side: 1148.912964502 Break this problem into two subproblems by setting (x + 1) equal to 1148.912964502 and -1148.912964502.Subproblem 1
x + 1 = 1148.912964502 Simplifying x + 1 = 1148.912964502 Reorder the terms: 1 + x = 1148.912964502 Solving 1 + x = 1148.912964502 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 = 1148.912964502 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1148.912964502 + -1 x = 1148.912964502 + -1 Combine like terms: 1148.912964502 + -1 = 1147.912964502 x = 1147.912964502 Simplifying x = 1147.912964502Subproblem 2
x + 1 = -1148.912964502 Simplifying x + 1 = -1148.912964502 Reorder the terms: 1 + x = -1148.912964502 Solving 1 + x = -1148.912964502 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 = -1148.912964502 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1148.912964502 + -1 x = -1148.912964502 + -1 Combine like terms: -1148.912964502 + -1 = -1149.912964502 x = -1149.912964502 Simplifying x = -1149.912964502Solution
The solution to the problem is based on the solutions from the subproblems. x = {1147.912964502, -1149.912964502}
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