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Simplifying 204 = x2 + 6x Reorder the terms: 204 = 6x + x2 Solving 204 = 6x + x2 Solving for variable 'x'. Reorder the terms: 204 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 204 + -6x + -1x2 = 0 + x2 + -1x2 204 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 204 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -204 + 6x + x2 = 0 Move the constant term to the right: Add '204' to each side of the equation. -204 + 6x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 6x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 6x + x2 = 0 + 204 6x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 6x + x2 = 204 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 204 + 9 Reorder the terms: 9 + 6x + x2 = 204 + 9 Combine like terms: 204 + 9 = 213 9 + 6x + x2 = 213 Factor a perfect square on the left side: (x + 3)(x + 3) = 213 Calculate the square root of the right side: 14.594519519 Break this problem into two subproblems by setting (x + 3) equal to 14.594519519 and -14.594519519.Subproblem 1
x + 3 = 14.594519519 Simplifying x + 3 = 14.594519519 Reorder the terms: 3 + x = 14.594519519 Solving 3 + x = 14.594519519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 14.594519519 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.594519519 + -3 x = 14.594519519 + -3 Combine like terms: 14.594519519 + -3 = 11.594519519 x = 11.594519519 Simplifying x = 11.594519519Subproblem 2
x + 3 = -14.594519519 Simplifying x + 3 = -14.594519519 Reorder the terms: 3 + x = -14.594519519 Solving 3 + x = -14.594519519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -14.594519519 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.594519519 + -3 x = -14.594519519 + -3 Combine like terms: -14.594519519 + -3 = -17.594519519 x = -17.594519519 Simplifying x = -17.594519519Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.594519519, -17.594519519}
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