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Simplifying x2 + 80x + -195 = 0 Reorder the terms: -195 + 80x + x2 = 0 Solving -195 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '195' to each side of the equation. -195 + 80x + 195 + x2 = 0 + 195 Reorder the terms: -195 + 195 + 80x + x2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + 80x + x2 = 0 + 195 80x + x2 = 0 + 195 Combine like terms: 0 + 195 = 195 80x + x2 = 195 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 195 + 1600 Reorder the terms: 1600 + 80x + x2 = 195 + 1600 Combine like terms: 195 + 1600 = 1795 1600 + 80x + x2 = 1795 Factor a perfect square on the left side: (x + 40)(x + 40) = 1795 Calculate the square root of the right side: 42.367440329 Break this problem into two subproblems by setting (x + 40) equal to 42.367440329 and -42.367440329.Subproblem 1
x + 40 = 42.367440329 Simplifying x + 40 = 42.367440329 Reorder the terms: 40 + x = 42.367440329 Solving 40 + x = 42.367440329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 42.367440329 + -40 Combine like terms: 40 + -40 = 0 0 + x = 42.367440329 + -40 x = 42.367440329 + -40 Combine like terms: 42.367440329 + -40 = 2.367440329 x = 2.367440329 Simplifying x = 2.367440329Subproblem 2
x + 40 = -42.367440329 Simplifying x + 40 = -42.367440329 Reorder the terms: 40 + x = -42.367440329 Solving 40 + x = -42.367440329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -42.367440329 + -40 Combine like terms: 40 + -40 = 0 0 + x = -42.367440329 + -40 x = -42.367440329 + -40 Combine like terms: -42.367440329 + -40 = -82.367440329 x = -82.367440329 Simplifying x = -82.367440329Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.367440329, -82.367440329}
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