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Simplifying 0.60x2 + -6x + -6000 = 0 Reorder the terms: -6000 + -6x + 0.60x2 = 0 Solving -6000 + -6x + 0.60x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.60 the coefficient of the squared term: Divide each side by '0.60'. -10000 + -10x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + -10x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + -10x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + -10x + x2 = 0 + 10000 -10x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 -10x + x2 = 10000 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 = 10000 + 25 Reorder the terms: 25 + -10x + x2 = 10000 + 25 Combine like terms: 10000 + 25 = 10025 25 + -10x + x2 = 10025 Factor a perfect square on the left side: (x + -5)(x + -5) = 10025 Calculate the square root of the right side: 100.124921973 Break this problem into two subproblems by setting (x + -5) equal to 100.124921973 and -100.124921973.Subproblem 1
x + -5 = 100.124921973 Simplifying x + -5 = 100.124921973 Reorder the terms: -5 + x = 100.124921973 Solving -5 + x = 100.124921973 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 = 100.124921973 + 5 Combine like terms: -5 + 5 = 0 0 + x = 100.124921973 + 5 x = 100.124921973 + 5 Combine like terms: 100.124921973 + 5 = 105.124921973 x = 105.124921973 Simplifying x = 105.124921973Subproblem 2
x + -5 = -100.124921973 Simplifying x + -5 = -100.124921973 Reorder the terms: -5 + x = -100.124921973 Solving -5 + x = -100.124921973 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 = -100.124921973 + 5 Combine like terms: -5 + 5 = 0 0 + x = -100.124921973 + 5 x = -100.124921973 + 5 Combine like terms: -100.124921973 + 5 = -95.124921973 x = -95.124921973 Simplifying x = -95.124921973Solution
The solution to the problem is based on the solutions from the subproblems. x = {105.124921973, -95.124921973}
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