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Simplifying x2 + -3x + -960 = 0 Reorder the terms: -960 + -3x + x2 = 0 Solving -960 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '960' to each side of the equation. -960 + -3x + 960 + x2 = 0 + 960 Reorder the terms: -960 + 960 + -3x + x2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + -3x + x2 = 0 + 960 -3x + x2 = 0 + 960 Combine like terms: 0 + 960 = 960 -3x + x2 = 960 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 = 960 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 960 + 2.25 Combine like terms: 960 + 2.25 = 962.25 2.25 + -3x + x2 = 962.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 962.25 Calculate the square root of the right side: 31.020154738 Break this problem into two subproblems by setting (x + -1.5) equal to 31.020154738 and -31.020154738.Subproblem 1
x + -1.5 = 31.020154738 Simplifying x + -1.5 = 31.020154738 Reorder the terms: -1.5 + x = 31.020154738 Solving -1.5 + x = 31.020154738 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 = 31.020154738 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 31.020154738 + 1.5 x = 31.020154738 + 1.5 Combine like terms: 31.020154738 + 1.5 = 32.520154738 x = 32.520154738 Simplifying x = 32.520154738Subproblem 2
x + -1.5 = -31.020154738 Simplifying x + -1.5 = -31.020154738 Reorder the terms: -1.5 + x = -31.020154738 Solving -1.5 + x = -31.020154738 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 = -31.020154738 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -31.020154738 + 1.5 x = -31.020154738 + 1.5 Combine like terms: -31.020154738 + 1.5 = -29.520154738 x = -29.520154738 Simplifying x = -29.520154738Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.520154738, -29.520154738}
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