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Simplifying (x2 + 6x + -1200) = 0 Reorder the terms: (-1200 + 6x + x2) = 0 Remove parenthesis around (-1200 + 6x + x2) -1200 + 6x + x2 = 0 Solving -1200 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 6x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 6x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 6x + x2 = 0 + 1200 6x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 6x + x2 = 1200 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 = 1200 + 9 Reorder the terms: 9 + 6x + x2 = 1200 + 9 Combine like terms: 1200 + 9 = 1209 9 + 6x + x2 = 1209 Factor a perfect square on the left side: (x + 3)(x + 3) = 1209 Calculate the square root of the right side: 34.770677301 Break this problem into two subproblems by setting (x + 3) equal to 34.770677301 and -34.770677301.Subproblem 1
x + 3 = 34.770677301 Simplifying x + 3 = 34.770677301 Reorder the terms: 3 + x = 34.770677301 Solving 3 + x = 34.770677301 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 = 34.770677301 + -3 Combine like terms: 3 + -3 = 0 0 + x = 34.770677301 + -3 x = 34.770677301 + -3 Combine like terms: 34.770677301 + -3 = 31.770677301 x = 31.770677301 Simplifying x = 31.770677301Subproblem 2
x + 3 = -34.770677301 Simplifying x + 3 = -34.770677301 Reorder the terms: 3 + x = -34.770677301 Solving 3 + x = -34.770677301 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 = -34.770677301 + -3 Combine like terms: 3 + -3 = 0 0 + x = -34.770677301 + -3 x = -34.770677301 + -3 Combine like terms: -34.770677301 + -3 = -37.770677301 x = -37.770677301 Simplifying x = -37.770677301Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.770677301, -37.770677301}
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