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Simplifying x2 + 6x + -2322 = 0 Reorder the terms: -2322 + 6x + x2 = 0 Solving -2322 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2322' to each side of the equation. -2322 + 6x + 2322 + x2 = 0 + 2322 Reorder the terms: -2322 + 2322 + 6x + x2 = 0 + 2322 Combine like terms: -2322 + 2322 = 0 0 + 6x + x2 = 0 + 2322 6x + x2 = 0 + 2322 Combine like terms: 0 + 2322 = 2322 6x + x2 = 2322 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 = 2322 + 9 Reorder the terms: 9 + 6x + x2 = 2322 + 9 Combine like terms: 2322 + 9 = 2331 9 + 6x + x2 = 2331 Factor a perfect square on the left side: (x + 3)(x + 3) = 2331 Calculate the square root of the right side: 48.280430818 Break this problem into two subproblems by setting (x + 3) equal to 48.280430818 and -48.280430818.Subproblem 1
x + 3 = 48.280430818 Simplifying x + 3 = 48.280430818 Reorder the terms: 3 + x = 48.280430818 Solving 3 + x = 48.280430818 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 = 48.280430818 + -3 Combine like terms: 3 + -3 = 0 0 + x = 48.280430818 + -3 x = 48.280430818 + -3 Combine like terms: 48.280430818 + -3 = 45.280430818 x = 45.280430818 Simplifying x = 45.280430818Subproblem 2
x + 3 = -48.280430818 Simplifying x + 3 = -48.280430818 Reorder the terms: 3 + x = -48.280430818 Solving 3 + x = -48.280430818 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 = -48.280430818 + -3 Combine like terms: 3 + -3 = 0 0 + x = -48.280430818 + -3 x = -48.280430818 + -3 Combine like terms: -48.280430818 + -3 = -51.280430818 x = -51.280430818 Simplifying x = -51.280430818Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.280430818, -51.280430818}
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