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Simplifying x2 + -10x + 27 = 6000 Reorder the terms: 27 + -10x + x2 = 6000 Solving 27 + -10x + x2 = 6000 Solving for variable 'x'. Reorder the terms: 27 + -6000 + -10x + x2 = 6000 + -6000 Combine like terms: 27 + -6000 = -5973 -5973 + -10x + x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -5973 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5973' to each side of the equation. -5973 + -10x + 5973 + x2 = 0 + 5973 Reorder the terms: -5973 + 5973 + -10x + x2 = 0 + 5973 Combine like terms: -5973 + 5973 = 0 0 + -10x + x2 = 0 + 5973 -10x + x2 = 0 + 5973 Combine like terms: 0 + 5973 = 5973 -10x + x2 = 5973 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 5973 + 25 Reorder the terms: 25 + -10x + x2 = 5973 + 25 Combine like terms: 5973 + 25 = 5998 25 + -10x + x2 = 5998 Factor a perfect square on the left side: (x + -5)(x + -5) = 5998 Calculate the square root of the right side: 77.446755904 Break this problem into two subproblems by setting (x + -5) equal to 77.446755904 and -77.446755904.Subproblem 1
x + -5 = 77.446755904 Simplifying x + -5 = 77.446755904 Reorder the terms: -5 + x = 77.446755904 Solving -5 + x = 77.446755904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 77.446755904 + 5 Combine like terms: -5 + 5 = 0 0 + x = 77.446755904 + 5 x = 77.446755904 + 5 Combine like terms: 77.446755904 + 5 = 82.446755904 x = 82.446755904 Simplifying x = 82.446755904Subproblem 2
x + -5 = -77.446755904 Simplifying x + -5 = -77.446755904 Reorder the terms: -5 + x = -77.446755904 Solving -5 + x = -77.446755904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -77.446755904 + 5 Combine like terms: -5 + 5 = 0 0 + x = -77.446755904 + 5 x = -77.446755904 + 5 Combine like terms: -77.446755904 + 5 = -72.446755904 x = -72.446755904 Simplifying x = -72.446755904Solution
The solution to the problem is based on the solutions from the subproblems. x = {82.446755904, -72.446755904}
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