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Simplifying x2 + 6x + -1850 = 0 Reorder the terms: -1850 + 6x + x2 = 0 Solving -1850 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1850' to each side of the equation. -1850 + 6x + 1850 + x2 = 0 + 1850 Reorder the terms: -1850 + 1850 + 6x + x2 = 0 + 1850 Combine like terms: -1850 + 1850 = 0 0 + 6x + x2 = 0 + 1850 6x + x2 = 0 + 1850 Combine like terms: 0 + 1850 = 1850 6x + x2 = 1850 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 = 1850 + 9 Reorder the terms: 9 + 6x + x2 = 1850 + 9 Combine like terms: 1850 + 9 = 1859 9 + 6x + x2 = 1859 Factor a perfect square on the left side: (x + 3)(x + 3) = 1859 Calculate the square root of the right side: 43.116122275 Break this problem into two subproblems by setting (x + 3) equal to 43.116122275 and -43.116122275.Subproblem 1
x + 3 = 43.116122275 Simplifying x + 3 = 43.116122275 Reorder the terms: 3 + x = 43.116122275 Solving 3 + x = 43.116122275 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 = 43.116122275 + -3 Combine like terms: 3 + -3 = 0 0 + x = 43.116122275 + -3 x = 43.116122275 + -3 Combine like terms: 43.116122275 + -3 = 40.116122275 x = 40.116122275 Simplifying x = 40.116122275Subproblem 2
x + 3 = -43.116122275 Simplifying x + 3 = -43.116122275 Reorder the terms: 3 + x = -43.116122275 Solving 3 + x = -43.116122275 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 = -43.116122275 + -3 Combine like terms: 3 + -3 = 0 0 + x = -43.116122275 + -3 x = -43.116122275 + -3 Combine like terms: -43.116122275 + -3 = -46.116122275 x = -46.116122275 Simplifying x = -46.116122275Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.116122275, -46.116122275}
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