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Simplifying 3x(x + 18) = 256 Reorder the terms: 3x(18 + x) = 256 (18 * 3x + x * 3x) = 256 (54x + 3x2) = 256 Solving 54x + 3x2 = 256 Solving for variable 'x'. Reorder the terms: -256 + 54x + 3x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -256 + 54x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -85.33333333 + 18x + x2 = 0 Move the constant term to the right: Add '85.33333333' to each side of the equation. -85.33333333 + 18x + 85.33333333 + x2 = 0 + 85.33333333 Reorder the terms: -85.33333333 + 85.33333333 + 18x + x2 = 0 + 85.33333333 Combine like terms: -85.33333333 + 85.33333333 = 0.00000000 0.00000000 + 18x + x2 = 0 + 85.33333333 18x + x2 = 0 + 85.33333333 Combine like terms: 0 + 85.33333333 = 85.33333333 18x + x2 = 85.33333333 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 = 85.33333333 + 81 Reorder the terms: 81 + 18x + x2 = 85.33333333 + 81 Combine like terms: 85.33333333 + 81 = 166.33333333 81 + 18x + x2 = 166.33333333 Factor a perfect square on the left side: (x + 9)(x + 9) = 166.33333333 Calculate the square root of the right side: 12.897028081 Break this problem into two subproblems by setting (x + 9) equal to 12.897028081 and -12.897028081.Subproblem 1
x + 9 = 12.897028081 Simplifying x + 9 = 12.897028081 Reorder the terms: 9 + x = 12.897028081 Solving 9 + x = 12.897028081 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 = 12.897028081 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.897028081 + -9 x = 12.897028081 + -9 Combine like terms: 12.897028081 + -9 = 3.897028081 x = 3.897028081 Simplifying x = 3.897028081Subproblem 2
x + 9 = -12.897028081 Simplifying x + 9 = -12.897028081 Reorder the terms: 9 + x = -12.897028081 Solving 9 + x = -12.897028081 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 = -12.897028081 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.897028081 + -9 x = -12.897028081 + -9 Combine like terms: -12.897028081 + -9 = -21.897028081 x = -21.897028081 Simplifying x = -21.897028081Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.897028081, -21.897028081}
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