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Simplifying 8400 = (x + 100)(x + 59) Reorder the terms: 8400 = (100 + x)(x + 59) Reorder the terms: 8400 = (100 + x)(59 + x) Multiply (100 + x) * (59 + x) 8400 = (100(59 + x) + x(59 + x)) 8400 = ((59 * 100 + x * 100) + x(59 + x)) 8400 = ((5900 + 100x) + x(59 + x)) 8400 = (5900 + 100x + (59 * x + x * x)) 8400 = (5900 + 100x + (59x + x2)) Combine like terms: 100x + 59x = 159x 8400 = (5900 + 159x + x2) Solving 8400 = 5900 + 159x + x2 Solving for variable 'x'. Combine like terms: 8400 + -5900 = 2500 2500 + -159x + -1x2 = 5900 + 159x + x2 + -5900 + -159x + -1x2 Reorder the terms: 2500 + -159x + -1x2 = 5900 + -5900 + 159x + -159x + x2 + -1x2 Combine like terms: 5900 + -5900 = 0 2500 + -159x + -1x2 = 0 + 159x + -159x + x2 + -1x2 2500 + -159x + -1x2 = 159x + -159x + x2 + -1x2 Combine like terms: 159x + -159x = 0 2500 + -159x + -1x2 = 0 + x2 + -1x2 2500 + -159x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2500 + -159x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2500 + 159x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 159x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 159x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 159x + x2 = 0 + 2500 159x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 159x + x2 = 2500 The x term is 159x. Take half its coefficient (79.5). Square it (6320.25) and add it to both sides. Add '6320.25' to each side of the equation. 159x + 6320.25 + x2 = 2500 + 6320.25 Reorder the terms: 6320.25 + 159x + x2 = 2500 + 6320.25 Combine like terms: 2500 + 6320.25 = 8820.25 6320.25 + 159x + x2 = 8820.25 Factor a perfect square on the left side: (x + 79.5)(x + 79.5) = 8820.25 Calculate the square root of the right side: 93.916186038 Break this problem into two subproblems by setting (x + 79.5) equal to 93.916186038 and -93.916186038.Subproblem 1
x + 79.5 = 93.916186038 Simplifying x + 79.5 = 93.916186038 Reorder the terms: 79.5 + x = 93.916186038 Solving 79.5 + x = 93.916186038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-79.5' to each side of the equation. 79.5 + -79.5 + x = 93.916186038 + -79.5 Combine like terms: 79.5 + -79.5 = 0.0 0.0 + x = 93.916186038 + -79.5 x = 93.916186038 + -79.5 Combine like terms: 93.916186038 + -79.5 = 14.416186038 x = 14.416186038 Simplifying x = 14.416186038Subproblem 2
x + 79.5 = -93.916186038 Simplifying x + 79.5 = -93.916186038 Reorder the terms: 79.5 + x = -93.916186038 Solving 79.5 + x = -93.916186038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-79.5' to each side of the equation. 79.5 + -79.5 + x = -93.916186038 + -79.5 Combine like terms: 79.5 + -79.5 = 0.0 0.0 + x = -93.916186038 + -79.5 x = -93.916186038 + -79.5 Combine like terms: -93.916186038 + -79.5 = -173.416186038 x = -173.416186038 Simplifying x = -173.416186038Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.416186038, -173.416186038}
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