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Simplifying 3563 = x2 + 10x + -2 Reorder the terms: 3563 = -2 + 10x + x2 Solving 3563 = -2 + 10x + x2 Solving for variable 'x'. Combine like terms: 3563 + 2 = 3565 3565 + -10x + -1x2 = -2 + 10x + x2 + 2 + -10x + -1x2 Reorder the terms: 3565 + -10x + -1x2 = -2 + 2 + 10x + -10x + x2 + -1x2 Combine like terms: -2 + 2 = 0 3565 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 3565 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 3565 + -10x + -1x2 = 0 + x2 + -1x2 3565 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3565 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3565 + 10x + x2 = 0 Move the constant term to the right: Add '3565' to each side of the equation. -3565 + 10x + 3565 + x2 = 0 + 3565 Reorder the terms: -3565 + 3565 + 10x + x2 = 0 + 3565 Combine like terms: -3565 + 3565 = 0 0 + 10x + x2 = 0 + 3565 10x + x2 = 0 + 3565 Combine like terms: 0 + 3565 = 3565 10x + x2 = 3565 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3565 + 25 Reorder the terms: 25 + 10x + x2 = 3565 + 25 Combine like terms: 3565 + 25 = 3590 25 + 10x + x2 = 3590 Factor a perfect square on the left side: (x + 5)(x + 5) = 3590 Calculate the square root of the right side: 59.916608716 Break this problem into two subproblems by setting (x + 5) equal to 59.916608716 and -59.916608716.Subproblem 1
x + 5 = 59.916608716 Simplifying x + 5 = 59.916608716 Reorder the terms: 5 + x = 59.916608716 Solving 5 + x = 59.916608716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 59.916608716 + -5 Combine like terms: 5 + -5 = 0 0 + x = 59.916608716 + -5 x = 59.916608716 + -5 Combine like terms: 59.916608716 + -5 = 54.916608716 x = 54.916608716 Simplifying x = 54.916608716Subproblem 2
x + 5 = -59.916608716 Simplifying x + 5 = -59.916608716 Reorder the terms: 5 + x = -59.916608716 Solving 5 + x = -59.916608716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -59.916608716 + -5 Combine like terms: 5 + -5 = 0 0 + x = -59.916608716 + -5 x = -59.916608716 + -5 Combine like terms: -59.916608716 + -5 = -64.916608716 x = -64.916608716 Simplifying x = -64.916608716Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.916608716, -64.916608716}
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