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Simplifying x2 + -3x + 2 = 6000 Reorder the terms: 2 + -3x + x2 = 6000 Solving 2 + -3x + x2 = 6000 Solving for variable 'x'. Reorder the terms: 2 + -6000 + -3x + x2 = 6000 + -6000 Combine like terms: 2 + -6000 = -5998 -5998 + -3x + x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -5998 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5998' to each side of the equation. -5998 + -3x + 5998 + x2 = 0 + 5998 Reorder the terms: -5998 + 5998 + -3x + x2 = 0 + 5998 Combine like terms: -5998 + 5998 = 0 0 + -3x + x2 = 0 + 5998 -3x + x2 = 0 + 5998 Combine like terms: 0 + 5998 = 5998 -3x + x2 = 5998 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 = 5998 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 5998 + 2.25 Combine like terms: 5998 + 2.25 = 6000.25 2.25 + -3x + x2 = 6000.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6000.25 Calculate the square root of the right side: 77.46128065 Break this problem into two subproblems by setting (x + -1.5) equal to 77.46128065 and -77.46128065.Subproblem 1
x + -1.5 = 77.46128065 Simplifying x + -1.5 = 77.46128065 Reorder the terms: -1.5 + x = 77.46128065 Solving -1.5 + x = 77.46128065 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 = 77.46128065 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 77.46128065 + 1.5 x = 77.46128065 + 1.5 Combine like terms: 77.46128065 + 1.5 = 78.96128065 x = 78.96128065 Simplifying x = 78.96128065Subproblem 2
x + -1.5 = -77.46128065 Simplifying x + -1.5 = -77.46128065 Reorder the terms: -1.5 + x = -77.46128065 Solving -1.5 + x = -77.46128065 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 = -77.46128065 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -77.46128065 + 1.5 x = -77.46128065 + 1.5 Combine like terms: -77.46128065 + 1.5 = -75.96128065 x = -75.96128065 Simplifying x = -75.96128065Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.96128065, -75.96128065}
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