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Simplifying 6x2 + 15x + -1100 = 0 Reorder the terms: -1100 + 15x + 6x2 = 0 Solving -1100 + 15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -183.3333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '183.3333333' to each side of the equation. -183.3333333 + 2.5x + 183.3333333 + x2 = 0 + 183.3333333 Reorder the terms: -183.3333333 + 183.3333333 + 2.5x + x2 = 0 + 183.3333333 Combine like terms: -183.3333333 + 183.3333333 = 0.0000000 0.0000000 + 2.5x + x2 = 0 + 183.3333333 2.5x + x2 = 0 + 183.3333333 Combine like terms: 0 + 183.3333333 = 183.3333333 2.5x + x2 = 183.3333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 183.3333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 183.3333333 + 1.5625 Combine like terms: 183.3333333 + 1.5625 = 184.8958333 1.5625 + 2.5x + x2 = 184.8958333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 184.8958333 Calculate the square root of the right side: 13.597640726 Break this problem into two subproblems by setting (x + 1.25) equal to 13.597640726 and -13.597640726.Subproblem 1
x + 1.25 = 13.597640726 Simplifying x + 1.25 = 13.597640726 Reorder the terms: 1.25 + x = 13.597640726 Solving 1.25 + x = 13.597640726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 13.597640726 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 13.597640726 + -1.25 x = 13.597640726 + -1.25 Combine like terms: 13.597640726 + -1.25 = 12.347640726 x = 12.347640726 Simplifying x = 12.347640726Subproblem 2
x + 1.25 = -13.597640726 Simplifying x + 1.25 = -13.597640726 Reorder the terms: 1.25 + x = -13.597640726 Solving 1.25 + x = -13.597640726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -13.597640726 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -13.597640726 + -1.25 x = -13.597640726 + -1.25 Combine like terms: -13.597640726 + -1.25 = -14.847640726 x = -14.847640726 Simplifying x = -14.847640726Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.347640726, -14.847640726}
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