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Simplifying x2 + -11x + -150 = 0 Reorder the terms: -150 + -11x + x2 = 0 Solving -150 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + -11x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -11x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -11x + x2 = 0 + 150 -11x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -11x + x2 = 150 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 150 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 150 + 30.25 Combine like terms: 150 + 30.25 = 180.25 30.25 + -11x + x2 = 180.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -5.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -5.5 = 13.425721582 Simplifying x + -5.5 = 13.425721582 Reorder the terms: -5.5 + x = 13.425721582 Solving -5.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 13.425721582 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 13.425721582 + 5.5 x = 13.425721582 + 5.5 Combine like terms: 13.425721582 + 5.5 = 18.925721582 x = 18.925721582 Simplifying x = 18.925721582Subproblem 2
x + -5.5 = -13.425721582 Simplifying x + -5.5 = -13.425721582 Reorder the terms: -5.5 + x = -13.425721582 Solving -5.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -13.425721582 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -13.425721582 + 5.5 x = -13.425721582 + 5.5 Combine like terms: -13.425721582 + 5.5 = -7.925721582 x = -7.925721582 Simplifying x = -7.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.925721582, -7.925721582}
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