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Simplifying x2 + 5x + -228 = 0 Reorder the terms: -228 + 5x + x2 = 0 Solving -228 + 5x + 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 + 5x + 228 + x2 = 0 + 228 Reorder the terms: -228 + 228 + 5x + x2 = 0 + 228 Combine like terms: -228 + 228 = 0 0 + 5x + x2 = 0 + 228 5x + x2 = 0 + 228 Combine like terms: 0 + 228 = 228 5x + x2 = 228 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 228 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 228 + 6.25 Combine like terms: 228 + 6.25 = 234.25 6.25 + 5x + x2 = 234.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 234.25 Calculate the square root of the right side: 15.305227865 Break this problem into two subproblems by setting (x + 2.5) equal to 15.305227865 and -15.305227865.Subproblem 1
x + 2.5 = 15.305227865 Simplifying x + 2.5 = 15.305227865 Reorder the terms: 2.5 + x = 15.305227865 Solving 2.5 + x = 15.305227865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 15.305227865 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 15.305227865 + -2.5 x = 15.305227865 + -2.5 Combine like terms: 15.305227865 + -2.5 = 12.805227865 x = 12.805227865 Simplifying x = 12.805227865Subproblem 2
x + 2.5 = -15.305227865 Simplifying x + 2.5 = -15.305227865 Reorder the terms: 2.5 + x = -15.305227865 Solving 2.5 + x = -15.305227865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -15.305227865 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -15.305227865 + -2.5 x = -15.305227865 + -2.5 Combine like terms: -15.305227865 + -2.5 = -17.805227865 x = -17.805227865 Simplifying x = -17.805227865Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.805227865, -17.805227865}
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