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Simplifying x2 + -150x + -4400 = 0 Reorder the terms: -4400 + -150x + x2 = 0 Solving -4400 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4400' to each side of the equation. -4400 + -150x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + -150x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + -150x + x2 = 0 + 4400 -150x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 -150x + x2 = 4400 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 = 4400 + 5625 Reorder the terms: 5625 + -150x + x2 = 4400 + 5625 Combine like terms: 4400 + 5625 = 10025 5625 + -150x + x2 = 10025 Factor a perfect square on the left side: (x + -75)(x + -75) = 10025 Calculate the square root of the right side: 100.124921973 Break this problem into two subproblems by setting (x + -75) equal to 100.124921973 and -100.124921973.Subproblem 1
x + -75 = 100.124921973 Simplifying x + -75 = 100.124921973 Reorder the terms: -75 + x = 100.124921973 Solving -75 + x = 100.124921973 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 = 100.124921973 + 75 Combine like terms: -75 + 75 = 0 0 + x = 100.124921973 + 75 x = 100.124921973 + 75 Combine like terms: 100.124921973 + 75 = 175.124921973 x = 175.124921973 Simplifying x = 175.124921973Subproblem 2
x + -75 = -100.124921973 Simplifying x + -75 = -100.124921973 Reorder the terms: -75 + x = -100.124921973 Solving -75 + x = -100.124921973 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 = -100.124921973 + 75 Combine like terms: -75 + 75 = 0 0 + x = -100.124921973 + 75 x = -100.124921973 + 75 Combine like terms: -100.124921973 + 75 = -25.124921973 x = -25.124921973 Simplifying x = -25.124921973Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.124921973, -25.124921973}
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