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Simplifying x(x + 820) = 7000 Reorder the terms: x(820 + x) = 7000 (820 * x + x * x) = 7000 (820x + x2) = 7000 Solving 820x + x2 = 7000 Solving for variable 'x'. Reorder the terms: -7000 + 820x + x2 = 7000 + -7000 Combine like terms: 7000 + -7000 = 0 -7000 + 820x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7000' to each side of the equation. -7000 + 820x + 7000 + x2 = 0 + 7000 Reorder the terms: -7000 + 7000 + 820x + x2 = 0 + 7000 Combine like terms: -7000 + 7000 = 0 0 + 820x + x2 = 0 + 7000 820x + x2 = 0 + 7000 Combine like terms: 0 + 7000 = 7000 820x + x2 = 7000 The x term is 820x. Take half its coefficient (410). Square it (168100) and add it to both sides. Add '168100' to each side of the equation. 820x + 168100 + x2 = 7000 + 168100 Reorder the terms: 168100 + 820x + x2 = 7000 + 168100 Combine like terms: 7000 + 168100 = 175100 168100 + 820x + x2 = 175100 Factor a perfect square on the left side: (x + 410)(x + 410) = 175100 Calculate the square root of the right side: 418.449519058 Break this problem into two subproblems by setting (x + 410) equal to 418.449519058 and -418.449519058.Subproblem 1
x + 410 = 418.449519058 Simplifying x + 410 = 418.449519058 Reorder the terms: 410 + x = 418.449519058 Solving 410 + x = 418.449519058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-410' to each side of the equation. 410 + -410 + x = 418.449519058 + -410 Combine like terms: 410 + -410 = 0 0 + x = 418.449519058 + -410 x = 418.449519058 + -410 Combine like terms: 418.449519058 + -410 = 8.449519058 x = 8.449519058 Simplifying x = 8.449519058Subproblem 2
x + 410 = -418.449519058 Simplifying x + 410 = -418.449519058 Reorder the terms: 410 + x = -418.449519058 Solving 410 + x = -418.449519058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-410' to each side of the equation. 410 + -410 + x = -418.449519058 + -410 Combine like terms: 410 + -410 = 0 0 + x = -418.449519058 + -410 x = -418.449519058 + -410 Combine like terms: -418.449519058 + -410 = -828.449519058 x = -828.449519058 Simplifying x = -828.449519058Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.449519058, -828.449519058}
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