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Simplifying 2632 = x2 + 39x Reorder the terms: 2632 = 39x + x2 Solving 2632 = 39x + x2 Solving for variable 'x'. Reorder the terms: 2632 + -39x + -1x2 = 39x + -39x + x2 + -1x2 Combine like terms: 39x + -39x = 0 2632 + -39x + -1x2 = 0 + x2 + -1x2 2632 + -39x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2632 + -39x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2632 + 39x + x2 = 0 Move the constant term to the right: Add '2632' to each side of the equation. -2632 + 39x + 2632 + x2 = 0 + 2632 Reorder the terms: -2632 + 2632 + 39x + x2 = 0 + 2632 Combine like terms: -2632 + 2632 = 0 0 + 39x + x2 = 0 + 2632 39x + x2 = 0 + 2632 Combine like terms: 0 + 2632 = 2632 39x + x2 = 2632 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = 2632 + 380.25 Reorder the terms: 380.25 + 39x + x2 = 2632 + 380.25 Combine like terms: 2632 + 380.25 = 3012.25 380.25 + 39x + x2 = 3012.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 3012.25 Calculate the square root of the right side: 54.883968515 Break this problem into two subproblems by setting (x + 19.5) equal to 54.883968515 and -54.883968515.Subproblem 1
x + 19.5 = 54.883968515 Simplifying x + 19.5 = 54.883968515 Reorder the terms: 19.5 + x = 54.883968515 Solving 19.5 + x = 54.883968515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 54.883968515 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 54.883968515 + -19.5 x = 54.883968515 + -19.5 Combine like terms: 54.883968515 + -19.5 = 35.383968515 x = 35.383968515 Simplifying x = 35.383968515Subproblem 2
x + 19.5 = -54.883968515 Simplifying x + 19.5 = -54.883968515 Reorder the terms: 19.5 + x = -54.883968515 Solving 19.5 + x = -54.883968515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -54.883968515 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -54.883968515 + -19.5 x = -54.883968515 + -19.5 Combine like terms: -54.883968515 + -19.5 = -74.383968515 x = -74.383968515 Simplifying x = -74.383968515Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.383968515, -74.383968515}
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