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Simplifying x2 + -3x + -1680 = 0 Reorder the terms: -1680 + -3x + x2 = 0 Solving -1680 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1680' to each side of the equation. -1680 + -3x + 1680 + x2 = 0 + 1680 Reorder the terms: -1680 + 1680 + -3x + x2 = 0 + 1680 Combine like terms: -1680 + 1680 = 0 0 + -3x + x2 = 0 + 1680 -3x + x2 = 0 + 1680 Combine like terms: 0 + 1680 = 1680 -3x + x2 = 1680 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 = 1680 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1680 + 2.25 Combine like terms: 1680 + 2.25 = 1682.25 2.25 + -3x + x2 = 1682.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1682.25 Calculate the square root of the right side: 41.01524107 Break this problem into two subproblems by setting (x + -1.5) equal to 41.01524107 and -41.01524107.Subproblem 1
x + -1.5 = 41.01524107 Simplifying x + -1.5 = 41.01524107 Reorder the terms: -1.5 + x = 41.01524107 Solving -1.5 + x = 41.01524107 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 = 41.01524107 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 41.01524107 + 1.5 x = 41.01524107 + 1.5 Combine like terms: 41.01524107 + 1.5 = 42.51524107 x = 42.51524107 Simplifying x = 42.51524107Subproblem 2
x + -1.5 = -41.01524107 Simplifying x + -1.5 = -41.01524107 Reorder the terms: -1.5 + x = -41.01524107 Solving -1.5 + x = -41.01524107 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 = -41.01524107 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -41.01524107 + 1.5 x = -41.01524107 + 1.5 Combine like terms: -41.01524107 + 1.5 = -39.51524107 x = -39.51524107 Simplifying x = -39.51524107Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.51524107, -39.51524107}
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