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Simplifying x2 + -3x + -221 = 0 Reorder the terms: -221 + -3x + x2 = 0 Solving -221 + -3x + x2 = 0 Solving for variable 'x'. 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 = 16.441552797 x = 16.441552797 Simplifying x = 16.441552797Subproblem 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 = -13.441552797 x = -13.441552797 Simplifying x = -13.441552797Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.441552797, -13.441552797}
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