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Simplifying x2 + 165x + -2100 = 0 Reorder the terms: -2100 + 165x + x2 = 0 Solving -2100 + 165x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2100' to each side of the equation. -2100 + 165x + 2100 + x2 = 0 + 2100 Reorder the terms: -2100 + 2100 + 165x + x2 = 0 + 2100 Combine like terms: -2100 + 2100 = 0 0 + 165x + x2 = 0 + 2100 165x + x2 = 0 + 2100 Combine like terms: 0 + 2100 = 2100 165x + x2 = 2100 The x term is 165x. Take half its coefficient (82.5). Square it (6806.25) and add it to both sides. Add '6806.25' to each side of the equation. 165x + 6806.25 + x2 = 2100 + 6806.25 Reorder the terms: 6806.25 + 165x + x2 = 2100 + 6806.25 Combine like terms: 2100 + 6806.25 = 8906.25 6806.25 + 165x + x2 = 8906.25 Factor a perfect square on the left side: (x + 82.5)(x + 82.5) = 8906.25 Calculate the square root of the right side: 94.372930441 Break this problem into two subproblems by setting (x + 82.5) equal to 94.372930441 and -94.372930441.Subproblem 1
x + 82.5 = 94.372930441 Simplifying x + 82.5 = 94.372930441 Reorder the terms: 82.5 + x = 94.372930441 Solving 82.5 + x = 94.372930441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-82.5' to each side of the equation. 82.5 + -82.5 + x = 94.372930441 + -82.5 Combine like terms: 82.5 + -82.5 = 0.0 0.0 + x = 94.372930441 + -82.5 x = 94.372930441 + -82.5 Combine like terms: 94.372930441 + -82.5 = 11.872930441 x = 11.872930441 Simplifying x = 11.872930441Subproblem 2
x + 82.5 = -94.372930441 Simplifying x + 82.5 = -94.372930441 Reorder the terms: 82.5 + x = -94.372930441 Solving 82.5 + x = -94.372930441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-82.5' to each side of the equation. 82.5 + -82.5 + x = -94.372930441 + -82.5 Combine like terms: 82.5 + -82.5 = 0.0 0.0 + x = -94.372930441 + -82.5 x = -94.372930441 + -82.5 Combine like terms: -94.372930441 + -82.5 = -176.872930441 x = -176.872930441 Simplifying x = -176.872930441Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.872930441, -176.872930441}
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