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Simplifying x2 + -3x + -1440 = 0 Reorder the terms: -1440 + -3x + x2 = 0 Solving -1440 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1440' to each side of the equation. -1440 + -3x + 1440 + x2 = 0 + 1440 Reorder the terms: -1440 + 1440 + -3x + x2 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + -3x + x2 = 0 + 1440 -3x + x2 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 -3x + x2 = 1440 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 1440 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1440 + 2.25 Combine like terms: 1440 + 2.25 = 1442.25 2.25 + -3x + x2 = 1442.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1442.25 Calculate the square root of the right side: 37.976966704 Break this problem into two subproblems by setting (x + -1.5) equal to 37.976966704 and -37.976966704.Subproblem 1
x + -1.5 = 37.976966704 Simplifying x + -1.5 = 37.976966704 Reorder the terms: -1.5 + x = 37.976966704 Solving -1.5 + x = 37.976966704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 37.976966704 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 37.976966704 + 1.5 x = 37.976966704 + 1.5 Combine like terms: 37.976966704 + 1.5 = 39.476966704 x = 39.476966704 Simplifying x = 39.476966704Subproblem 2
x + -1.5 = -37.976966704 Simplifying x + -1.5 = -37.976966704 Reorder the terms: -1.5 + x = -37.976966704 Solving -1.5 + x = -37.976966704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -37.976966704 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -37.976966704 + 1.5 x = -37.976966704 + 1.5 Combine like terms: -37.976966704 + 1.5 = -36.476966704 x = -36.476966704 Simplifying x = -36.476966704Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.476966704, -36.476966704}
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