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Simplifying 3x(x + 18) = 257 Reorder the terms: 3x(18 + x) = 257 (18 * 3x + x * 3x) = 257 (54x + 3x2) = 257 Solving 54x + 3x2 = 257 Solving for variable 'x'. Reorder the terms: -257 + 54x + 3x2 = 257 + -257 Combine like terms: 257 + -257 = 0 -257 + 54x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -85.66666667 + 18x + x2 = 0 Move the constant term to the right: Add '85.66666667' to each side of the equation. -85.66666667 + 18x + 85.66666667 + x2 = 0 + 85.66666667 Reorder the terms: -85.66666667 + 85.66666667 + 18x + x2 = 0 + 85.66666667 Combine like terms: -85.66666667 + 85.66666667 = 0.00000000 0.00000000 + 18x + x2 = 0 + 85.66666667 18x + x2 = 0 + 85.66666667 Combine like terms: 0 + 85.66666667 = 85.66666667 18x + x2 = 85.66666667 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 85.66666667 + 81 Reorder the terms: 81 + 18x + x2 = 85.66666667 + 81 Combine like terms: 85.66666667 + 81 = 166.66666667 81 + 18x + x2 = 166.66666667 Factor a perfect square on the left side: (x + 9)(x + 9) = 166.66666667 Calculate the square root of the right side: 12.909944487 Break this problem into two subproblems by setting (x + 9) equal to 12.909944487 and -12.909944487.Subproblem 1
x + 9 = 12.909944487 Simplifying x + 9 = 12.909944487 Reorder the terms: 9 + x = 12.909944487 Solving 9 + x = 12.909944487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 12.909944487 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.909944487 + -9 x = 12.909944487 + -9 Combine like terms: 12.909944487 + -9 = 3.909944487 x = 3.909944487 Simplifying x = 3.909944487Subproblem 2
x + 9 = -12.909944487 Simplifying x + 9 = -12.909944487 Reorder the terms: 9 + x = -12.909944487 Solving 9 + x = -12.909944487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -12.909944487 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.909944487 + -9 x = -12.909944487 + -9 Combine like terms: -12.909944487 + -9 = -21.909944487 x = -21.909944487 Simplifying x = -21.909944487Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.909944487, -21.909944487}
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