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Simplifying x2 + 150x + -43875 = 0 Reorder the terms: -43875 + 150x + x2 = 0 Solving -43875 + 150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '43875' to each side of the equation. -43875 + 150x + 43875 + x2 = 0 + 43875 Reorder the terms: -43875 + 43875 + 150x + x2 = 0 + 43875 Combine like terms: -43875 + 43875 = 0 0 + 150x + x2 = 0 + 43875 150x + x2 = 0 + 43875 Combine like terms: 0 + 43875 = 43875 150x + x2 = 43875 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 43875 + 5625 Reorder the terms: 5625 + 150x + x2 = 43875 + 5625 Combine like terms: 43875 + 5625 = 49500 5625 + 150x + x2 = 49500 Factor a perfect square on the left side: (x + 75)(x + 75) = 49500 Calculate the square root of the right side: 222.485954613 Break this problem into two subproblems by setting (x + 75) equal to 222.485954613 and -222.485954613.Subproblem 1
x + 75 = 222.485954613 Simplifying x + 75 = 222.485954613 Reorder the terms: 75 + x = 222.485954613 Solving 75 + x = 222.485954613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 222.485954613 + -75 Combine like terms: 75 + -75 = 0 0 + x = 222.485954613 + -75 x = 222.485954613 + -75 Combine like terms: 222.485954613 + -75 = 147.485954613 x = 147.485954613 Simplifying x = 147.485954613Subproblem 2
x + 75 = -222.485954613 Simplifying x + 75 = -222.485954613 Reorder the terms: 75 + x = -222.485954613 Solving 75 + x = -222.485954613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -222.485954613 + -75 Combine like terms: 75 + -75 = 0 0 + x = -222.485954613 + -75 x = -222.485954613 + -75 Combine like terms: -222.485954613 + -75 = -297.485954613 x = -297.485954613 Simplifying x = -297.485954613Solution
The solution to the problem is based on the solutions from the subproblems. x = {147.485954613, -297.485954613}
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