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Simplifying 2(x + 3) * x + 1 = 204 Reorder the terms: 2(3 + x) * x + 1 = 204 Reorder the terms for easier multiplication: 2x(3 + x) + 1 = 204 (3 * 2x + x * 2x) + 1 = 204 (6x + 2x2) + 1 = 204 Reorder the terms: 1 + 6x + 2x2 = 204 Solving 1 + 6x + 2x2 = 204 Solving for variable 'x'. Reorder the terms: 1 + -204 + 6x + 2x2 = 204 + -204 Combine like terms: 1 + -204 = -203 -203 + 6x + 2x2 = 204 + -204 Combine like terms: 204 + -204 = 0 -203 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -101.5 + 3x + x2 = 0 Move the constant term to the right: Add '101.5' to each side of the equation. -101.5 + 3x + 101.5 + x2 = 0 + 101.5 Reorder the terms: -101.5 + 101.5 + 3x + x2 = 0 + 101.5 Combine like terms: -101.5 + 101.5 = 0.0 0.0 + 3x + x2 = 0 + 101.5 3x + x2 = 0 + 101.5 Combine like terms: 0 + 101.5 = 101.5 3x + x2 = 101.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 101.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 101.5 + 2.25 Combine like terms: 101.5 + 2.25 = 103.75 2.25 + 3x + x2 = 103.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 103.75 Calculate the square root of the right side: 10.185774394 Break this problem into two subproblems by setting (x + 1.5) equal to 10.185774394 and -10.185774394.Subproblem 1
x + 1.5 = 10.185774394 Simplifying x + 1.5 = 10.185774394 Reorder the terms: 1.5 + x = 10.185774394 Solving 1.5 + x = 10.185774394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.185774394 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.185774394 + -1.5 x = 10.185774394 + -1.5 Combine like terms: 10.185774394 + -1.5 = 8.685774394 x = 8.685774394 Simplifying x = 8.685774394Subproblem 2
x + 1.5 = -10.185774394 Simplifying x + 1.5 = -10.185774394 Reorder the terms: 1.5 + x = -10.185774394 Solving 1.5 + x = -10.185774394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.185774394 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.185774394 + -1.5 x = -10.185774394 + -1.5 Combine like terms: -10.185774394 + -1.5 = -11.685774394 x = -11.685774394 Simplifying x = -11.685774394Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.685774394, -11.685774394}
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