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Simplifying x2 + 3x + -228 = 0 Reorder the terms: -228 + 3x + x2 = 0 Solving -228 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '228' to each side of the equation. -228 + 3x + 228 + x2 = 0 + 228 Reorder the terms: -228 + 228 + 3x + x2 = 0 + 228 Combine like terms: -228 + 228 = 0 0 + 3x + x2 = 0 + 228 3x + x2 = 0 + 228 Combine like terms: 0 + 228 = 228 3x + x2 = 228 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 = 228 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 228 + 2.25 Combine like terms: 228 + 2.25 = 230.25 2.25 + 3x + x2 = 230.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (x + 1.5) equal to 15.173990905 and -15.173990905.Subproblem 1
x + 1.5 = 15.173990905 Simplifying x + 1.5 = 15.173990905 Reorder the terms: 1.5 + x = 15.173990905 Solving 1.5 + x = 15.173990905 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 = 15.173990905 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.173990905 + -1.5 x = 15.173990905 + -1.5 Combine like terms: 15.173990905 + -1.5 = 13.673990905 x = 13.673990905 Simplifying x = 13.673990905Subproblem 2
x + 1.5 = -15.173990905 Simplifying x + 1.5 = -15.173990905 Reorder the terms: 1.5 + x = -15.173990905 Solving 1.5 + x = -15.173990905 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 = -15.173990905 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.173990905 + -1.5 x = -15.173990905 + -1.5 Combine like terms: -15.173990905 + -1.5 = -16.673990905 x = -16.673990905 Simplifying x = -16.673990905Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.673990905, -16.673990905}
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