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Simplifying x2 + -40x + 228 = 0 Reorder the terms: 228 + -40x + x2 = 0 Solving 228 + -40x + 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 + -40x + -228 + x2 = 0 + -228 Reorder the terms: 228 + -228 + -40x + x2 = 0 + -228 Combine like terms: 228 + -228 = 0 0 + -40x + x2 = 0 + -228 -40x + x2 = 0 + -228 Combine like terms: 0 + -228 = -228 -40x + x2 = -228 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -228 + 400 Reorder the terms: 400 + -40x + x2 = -228 + 400 Combine like terms: -228 + 400 = 172 400 + -40x + x2 = 172 Factor a perfect square on the left side: (x + -20)(x + -20) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + -20) equal to 13.114877049 and -13.114877049.Subproblem 1
x + -20 = 13.114877049 Simplifying x + -20 = 13.114877049 Reorder the terms: -20 + x = 13.114877049 Solving -20 + x = 13.114877049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 13.114877049 + 20 Combine like terms: -20 + 20 = 0 0 + x = 13.114877049 + 20 x = 13.114877049 + 20 Combine like terms: 13.114877049 + 20 = 33.114877049 x = 33.114877049 Simplifying x = 33.114877049Subproblem 2
x + -20 = -13.114877049 Simplifying x + -20 = -13.114877049 Reorder the terms: -20 + x = -13.114877049 Solving -20 + x = -13.114877049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -13.114877049 + 20 Combine like terms: -20 + 20 = 0 0 + x = -13.114877049 + 20 x = -13.114877049 + 20 Combine like terms: -13.114877049 + 20 = 6.885122951 x = 6.885122951 Simplifying x = 6.885122951Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.114877049, 6.885122951}
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