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Simplifying 0 = x2 + -6x + -800 Reorder the terms: 0 = -800 + -6x + x2 Solving 0 = -800 + -6x + x2 Solving for variable 'x'. Combine like terms: 0 + 800 = 800 800 + 6x + -1x2 = -800 + -6x + x2 + 800 + 6x + -1x2 Reorder the terms: 800 + 6x + -1x2 = -800 + 800 + -6x + 6x + x2 + -1x2 Combine like terms: -800 + 800 = 0 800 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2 800 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 800 + 6x + -1x2 = 0 + x2 + -1x2 800 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 800 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -800 + -6x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + -6x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + -6x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -6x + x2 = 0 + 800 -6x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 -6x + x2 = 800 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 800 + 9 Reorder the terms: 9 + -6x + x2 = 800 + 9 Combine like terms: 800 + 9 = 809 9 + -6x + x2 = 809 Factor a perfect square on the left side: (x + -3)(x + -3) = 809 Calculate the square root of the right side: 28.442925307 Break this problem into two subproblems by setting (x + -3) equal to 28.442925307 and -28.442925307.Subproblem 1
x + -3 = 28.442925307 Simplifying x + -3 = 28.442925307 Reorder the terms: -3 + x = 28.442925307 Solving -3 + x = 28.442925307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 28.442925307 + 3 Combine like terms: -3 + 3 = 0 0 + x = 28.442925307 + 3 x = 28.442925307 + 3 Combine like terms: 28.442925307 + 3 = 31.442925307 x = 31.442925307 Simplifying x = 31.442925307Subproblem 2
x + -3 = -28.442925307 Simplifying x + -3 = -28.442925307 Reorder the terms: -3 + x = -28.442925307 Solving -3 + x = -28.442925307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -28.442925307 + 3 Combine like terms: -3 + 3 = 0 0 + x = -28.442925307 + 3 x = -28.442925307 + 3 Combine like terms: -28.442925307 + 3 = -25.442925307 x = -25.442925307 Simplifying x = -25.442925307Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.442925307, -25.442925307}
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