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Simplifying 19000 = x2 + x + 800 Reorder the terms: 19000 = 800 + x + x2 Solving 19000 = 800 + x + x2 Solving for variable 'x'. Combine like terms: 19000 + -800 = 18200 18200 + -1x + -1x2 = 800 + x + x2 + -800 + -1x + -1x2 Reorder the terms: 18200 + -1x + -1x2 = 800 + -800 + x + -1x + x2 + -1x2 Combine like terms: 800 + -800 = 0 18200 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2 18200 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 18200 + -1x + -1x2 = 0 + x2 + -1x2 18200 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18200 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18200 + x + x2 = 0 Move the constant term to the right: Add '18200' to each side of the equation. -18200 + x + 18200 + x2 = 0 + 18200 Reorder the terms: -18200 + 18200 + x + x2 = 0 + 18200 Combine like terms: -18200 + 18200 = 0 0 + x + x2 = 0 + 18200 x + x2 = 0 + 18200 Combine like terms: 0 + 18200 = 18200 x + x2 = 18200 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 18200 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 18200 + 0.25 Combine like terms: 18200 + 0.25 = 18200.25 1.25 + x2 = 18200.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18200.25 Calculate the square root of the right side: 134.908302191 Break this problem into two subproblems by setting (x + 0.5) equal to 134.908302191 and -134.908302191.Subproblem 1
x + 0.5 = 134.908302191 Simplifying x + 0.5 = 134.908302191 Reorder the terms: 0.5 + x = 134.908302191 Solving 0.5 + x = 134.908302191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 134.908302191 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 134.908302191 + -0.5 x = 134.908302191 + -0.5 Combine like terms: 134.908302191 + -0.5 = 134.408302191 x = 134.408302191 Simplifying x = 134.408302191Subproblem 2
x + 0.5 = -134.908302191 Simplifying x + 0.5 = -134.908302191 Reorder the terms: 0.5 + x = -134.908302191 Solving 0.5 + x = -134.908302191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -134.908302191 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -134.908302191 + -0.5 x = -134.908302191 + -0.5 Combine like terms: -134.908302191 + -0.5 = -135.408302191 x = -135.408302191 Simplifying x = -135.408302191Solution
The solution to the problem is based on the solutions from the subproblems. x = {134.408302191, -135.408302191}
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