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Simplifying 2x2 + 19x + -30000 = 0 Reorder the terms: -30000 + 19x + 2x2 = 0 Solving -30000 + 19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15000 + 9.5x + x2 = 0 Move the constant term to the right: Add '15000' to each side of the equation. -15000 + 9.5x + 15000 + x2 = 0 + 15000 Reorder the terms: -15000 + 15000 + 9.5x + x2 = 0 + 15000 Combine like terms: -15000 + 15000 = 0 0 + 9.5x + x2 = 0 + 15000 9.5x + x2 = 0 + 15000 Combine like terms: 0 + 15000 = 15000 9.5x + x2 = 15000 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 15000 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 15000 + 22.5625 Combine like terms: 15000 + 22.5625 = 15022.5625 22.5625 + 9.5x + x2 = 15022.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 15022.5625 Calculate the square root of the right side: 122.566563548 Break this problem into two subproblems by setting (x + 4.75) equal to 122.566563548 and -122.566563548.Subproblem 1
x + 4.75 = 122.566563548 Simplifying x + 4.75 = 122.566563548 Reorder the terms: 4.75 + x = 122.566563548 Solving 4.75 + x = 122.566563548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 122.566563548 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 122.566563548 + -4.75 x = 122.566563548 + -4.75 Combine like terms: 122.566563548 + -4.75 = 117.816563548 x = 117.816563548 Simplifying x = 117.816563548Subproblem 2
x + 4.75 = -122.566563548 Simplifying x + 4.75 = -122.566563548 Reorder the terms: 4.75 + x = -122.566563548 Solving 4.75 + x = -122.566563548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -122.566563548 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -122.566563548 + -4.75 x = -122.566563548 + -4.75 Combine like terms: -122.566563548 + -4.75 = -127.316563548 x = -127.316563548 Simplifying x = -127.316563548Solution
The solution to the problem is based on the solutions from the subproblems. x = {117.816563548, -127.316563548}
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