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Simplifying x2 + -3x + -2250 = 0 Reorder the terms: -2250 + -3x + x2 = 0 Solving -2250 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2250' to each side of the equation. -2250 + -3x + 2250 + x2 = 0 + 2250 Reorder the terms: -2250 + 2250 + -3x + x2 = 0 + 2250 Combine like terms: -2250 + 2250 = 0 0 + -3x + x2 = 0 + 2250 -3x + x2 = 0 + 2250 Combine like terms: 0 + 2250 = 2250 -3x + x2 = 2250 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 = 2250 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2250 + 2.25 Combine like terms: 2250 + 2.25 = 2252.25 2.25 + -3x + x2 = 2252.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2252.25 Calculate the square root of the right side: 47.457876059 Break this problem into two subproblems by setting (x + -1.5) equal to 47.457876059 and -47.457876059.Subproblem 1
x + -1.5 = 47.457876059 Simplifying x + -1.5 = 47.457876059 Reorder the terms: -1.5 + x = 47.457876059 Solving -1.5 + x = 47.457876059 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 = 47.457876059 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 47.457876059 + 1.5 x = 47.457876059 + 1.5 Combine like terms: 47.457876059 + 1.5 = 48.957876059 x = 48.957876059 Simplifying x = 48.957876059Subproblem 2
x + -1.5 = -47.457876059 Simplifying x + -1.5 = -47.457876059 Reorder the terms: -1.5 + x = -47.457876059 Solving -1.5 + x = -47.457876059 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 = -47.457876059 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -47.457876059 + 1.5 x = -47.457876059 + 1.5 Combine like terms: -47.457876059 + 1.5 = -45.957876059 x = -45.957876059 Simplifying x = -45.957876059Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.957876059, -45.957876059}
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