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Simplifying 2x2 + 21x + -16632 = 0 Reorder the terms: -16632 + 21x + 2x2 = 0 Solving -16632 + 21x + 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'. -8316 + 10.5x + x2 = 0 Move the constant term to the right: Add '8316' to each side of the equation. -8316 + 10.5x + 8316 + x2 = 0 + 8316 Reorder the terms: -8316 + 8316 + 10.5x + x2 = 0 + 8316 Combine like terms: -8316 + 8316 = 0 0 + 10.5x + x2 = 0 + 8316 10.5x + x2 = 0 + 8316 Combine like terms: 0 + 8316 = 8316 10.5x + x2 = 8316 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 8316 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 8316 + 27.5625 Combine like terms: 8316 + 27.5625 = 8343.5625 27.5625 + 10.5x + x2 = 8343.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 8343.5625 Calculate the square root of the right side: 91.343103188 Break this problem into two subproblems by setting (x + 5.25) equal to 91.343103188 and -91.343103188.Subproblem 1
x + 5.25 = 91.343103188 Simplifying x + 5.25 = 91.343103188 Reorder the terms: 5.25 + x = 91.343103188 Solving 5.25 + x = 91.343103188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 91.343103188 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 91.343103188 + -5.25 x = 91.343103188 + -5.25 Combine like terms: 91.343103188 + -5.25 = 86.093103188 x = 86.093103188 Simplifying x = 86.093103188Subproblem 2
x + 5.25 = -91.343103188 Simplifying x + 5.25 = -91.343103188 Reorder the terms: 5.25 + x = -91.343103188 Solving 5.25 + x = -91.343103188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -91.343103188 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -91.343103188 + -5.25 x = -91.343103188 + -5.25 Combine like terms: -91.343103188 + -5.25 = -96.593103188 x = -96.593103188 Simplifying x = -96.593103188Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.093103188, -96.593103188}
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