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Simplifying 25(36 + x2) = -16(200 + -40x + -1x2) (36 * 25 + x2 * 25) = -16(200 + -40x + -1x2) (900 + 25x2) = -16(200 + -40x + -1x2) 900 + 25x2 = (200 * -16 + -40x * -16 + -1x2 * -16) 900 + 25x2 = (-3200 + 640x + 16x2) Solving 900 + 25x2 = -3200 + 640x + 16x2 Solving for variable 'x'. Reorder the terms: 900 + 3200 + -640x + 25x2 + -16x2 = -3200 + 640x + 16x2 + 3200 + -640x + -16x2 Combine like terms: 900 + 3200 = 4100 4100 + -640x + 25x2 + -16x2 = -3200 + 640x + 16x2 + 3200 + -640x + -16x2 Combine like terms: 25x2 + -16x2 = 9x2 4100 + -640x + 9x2 = -3200 + 640x + 16x2 + 3200 + -640x + -16x2 Reorder the terms: 4100 + -640x + 9x2 = -3200 + 3200 + 640x + -640x + 16x2 + -16x2 Combine like terms: -3200 + 3200 = 0 4100 + -640x + 9x2 = 0 + 640x + -640x + 16x2 + -16x2 4100 + -640x + 9x2 = 640x + -640x + 16x2 + -16x2 Combine like terms: 640x + -640x = 0 4100 + -640x + 9x2 = 0 + 16x2 + -16x2 4100 + -640x + 9x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 4100 + -640x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 455.5555556 + -71.11111111x + x2 = 0 Move the constant term to the right: Add '-455.5555556' to each side of the equation. 455.5555556 + -71.11111111x + -455.5555556 + x2 = 0 + -455.5555556 Reorder the terms: 455.5555556 + -455.5555556 + -71.11111111x + x2 = 0 + -455.5555556 Combine like terms: 455.5555556 + -455.5555556 = 0.0000000 0.0000000 + -71.11111111x + x2 = 0 + -455.5555556 -71.11111111x + x2 = 0 + -455.5555556 Combine like terms: 0 + -455.5555556 = -455.5555556 -71.11111111x + x2 = -455.5555556 The x term is -71.11111111x. Take half its coefficient (-35.55555556). Square it (1264.197531) and add it to both sides. Add '1264.197531' to each side of the equation. -71.11111111x + 1264.197531 + x2 = -455.5555556 + 1264.197531 Reorder the terms: 1264.197531 + -71.11111111x + x2 = -455.5555556 + 1264.197531 Combine like terms: -455.5555556 + 1264.197531 = 808.6419754 1264.197531 + -71.11111111x + x2 = 808.6419754 Factor a perfect square on the left side: (x + -35.55555556)(x + -35.55555556) = 808.6419754 Calculate the square root of the right side: 28.436630873 Break this problem into two subproblems by setting (x + -35.55555556) equal to 28.436630873 and -28.436630873.Subproblem 1
x + -35.55555556 = 28.436630873 Simplifying x + -35.55555556 = 28.436630873 Reorder the terms: -35.55555556 + x = 28.436630873 Solving -35.55555556 + x = 28.436630873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.55555556' to each side of the equation. -35.55555556 + 35.55555556 + x = 28.436630873 + 35.55555556 Combine like terms: -35.55555556 + 35.55555556 = 0.00000000 0.00000000 + x = 28.436630873 + 35.55555556 x = 28.436630873 + 35.55555556 Combine like terms: 28.436630873 + 35.55555556 = 63.992186433 x = 63.992186433 Simplifying x = 63.992186433Subproblem 2
x + -35.55555556 = -28.436630873 Simplifying x + -35.55555556 = -28.436630873 Reorder the terms: -35.55555556 + x = -28.436630873 Solving -35.55555556 + x = -28.436630873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.55555556' to each side of the equation. -35.55555556 + 35.55555556 + x = -28.436630873 + 35.55555556 Combine like terms: -35.55555556 + 35.55555556 = 0.00000000 0.00000000 + x = -28.436630873 + 35.55555556 x = -28.436630873 + 35.55555556 Combine like terms: -28.436630873 + 35.55555556 = 7.118924687 x = 7.118924687 Simplifying x = 7.118924687Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.992186433, 7.118924687}
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