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Simplifying x(x + 3) = 221 Reorder the terms: x(3 + x) = 221 (3 * x + x * x) = 221 (3x + x2) = 221 Solving 3x + x2 = 221 Solving for variable 'x'. Reorder the terms: -221 + 3x + x2 = 221 + -221 Combine like terms: 221 + -221 = 0 -221 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '221' to each side of the equation. -221 + 3x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + 3x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + 3x + x2 = 0 + 221 3x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 3x + x2 = 221 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 = 221 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 221 + 2.25 Combine like terms: 221 + 2.25 = 223.25 2.25 + 3x + x2 = 223.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 223.25 Calculate the square root of the right side: 14.941552797 Break this problem into two subproblems by setting (x + 1.5) equal to 14.941552797 and -14.941552797.Subproblem 1
x + 1.5 = 14.941552797 Simplifying x + 1.5 = 14.941552797 Reorder the terms: 1.5 + x = 14.941552797 Solving 1.5 + x = 14.941552797 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 = 14.941552797 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.941552797 + -1.5 x = 14.941552797 + -1.5 Combine like terms: 14.941552797 + -1.5 = 13.441552797 x = 13.441552797 Simplifying x = 13.441552797Subproblem 2
x + 1.5 = -14.941552797 Simplifying x + 1.5 = -14.941552797 Reorder the terms: 1.5 + x = -14.941552797 Solving 1.5 + x = -14.941552797 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 = -14.941552797 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.941552797 + -1.5 x = -14.941552797 + -1.5 Combine like terms: -14.941552797 + -1.5 = -16.441552797 x = -16.441552797 Simplifying x = -16.441552797Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.441552797, -16.441552797}
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