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Simplifying x2 + 20x + -6000 = 0 Reorder the terms: -6000 + 20x + x2 = 0 Solving -6000 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6000' to each side of the equation. -6000 + 20x + 6000 + x2 = 0 + 6000 Reorder the terms: -6000 + 6000 + 20x + x2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + 20x + x2 = 0 + 6000 20x + x2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 20x + x2 = 6000 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 6000 + 100 Reorder the terms: 100 + 20x + x2 = 6000 + 100 Combine like terms: 6000 + 100 = 6100 100 + 20x + x2 = 6100 Factor a perfect square on the left side: (x + 10)(x + 10) = 6100 Calculate the square root of the right side: 78.102496759 Break this problem into two subproblems by setting (x + 10) equal to 78.102496759 and -78.102496759.Subproblem 1
x + 10 = 78.102496759 Simplifying x + 10 = 78.102496759 Reorder the terms: 10 + x = 78.102496759 Solving 10 + x = 78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 78.102496759 + -10 Combine like terms: 10 + -10 = 0 0 + x = 78.102496759 + -10 x = 78.102496759 + -10 Combine like terms: 78.102496759 + -10 = 68.102496759 x = 68.102496759 Simplifying x = 68.102496759Subproblem 2
x + 10 = -78.102496759 Simplifying x + 10 = -78.102496759 Reorder the terms: 10 + x = -78.102496759 Solving 10 + x = -78.102496759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -78.102496759 + -10 Combine like terms: 10 + -10 = 0 0 + x = -78.102496759 + -10 x = -78.102496759 + -10 Combine like terms: -78.102496759 + -10 = -88.102496759 x = -88.102496759 Simplifying x = -88.102496759Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.102496759, -88.102496759}
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