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Simplifying x2 + -300x + -1764 = 0 Reorder the terms: -1764 + -300x + x2 = 0 Solving -1764 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1764' to each side of the equation. -1764 + -300x + 1764 + x2 = 0 + 1764 Reorder the terms: -1764 + 1764 + -300x + x2 = 0 + 1764 Combine like terms: -1764 + 1764 = 0 0 + -300x + x2 = 0 + 1764 -300x + x2 = 0 + 1764 Combine like terms: 0 + 1764 = 1764 -300x + x2 = 1764 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = 1764 + 22500 Reorder the terms: 22500 + -300x + x2 = 1764 + 22500 Combine like terms: 1764 + 22500 = 24264 22500 + -300x + x2 = 24264 Factor a perfect square on the left side: (x + -150)(x + -150) = 24264 Calculate the square root of the right side: 155.769059829 Break this problem into two subproblems by setting (x + -150) equal to 155.769059829 and -155.769059829.Subproblem 1
x + -150 = 155.769059829 Simplifying x + -150 = 155.769059829 Reorder the terms: -150 + x = 155.769059829 Solving -150 + x = 155.769059829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 155.769059829 + 150 Combine like terms: -150 + 150 = 0 0 + x = 155.769059829 + 150 x = 155.769059829 + 150 Combine like terms: 155.769059829 + 150 = 305.769059829 x = 305.769059829 Simplifying x = 305.769059829Subproblem 2
x + -150 = -155.769059829 Simplifying x + -150 = -155.769059829 Reorder the terms: -150 + x = -155.769059829 Solving -150 + x = -155.769059829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -155.769059829 + 150 Combine like terms: -150 + 150 = 0 0 + x = -155.769059829 + 150 x = -155.769059829 + 150 Combine like terms: -155.769059829 + 150 = -5.769059829 x = -5.769059829 Simplifying x = -5.769059829Solution
The solution to the problem is based on the solutions from the subproblems. x = {305.769059829, -5.769059829}
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