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Simplifying (x + 3)(x + 23 + 3) = 360 Reorder the terms: (3 + x)(x + 23 + 3) = 360 Reorder the terms: (3 + x)(23 + 3 + x) = 360 Combine like terms: 23 + 3 = 26 (3 + x)(26 + x) = 360 Multiply (3 + x) * (26 + x) (3(26 + x) + x(26 + x)) = 360 ((26 * 3 + x * 3) + x(26 + x)) = 360 ((78 + 3x) + x(26 + x)) = 360 (78 + 3x + (26 * x + x * x)) = 360 (78 + 3x + (26x + x2)) = 360 Combine like terms: 3x + 26x = 29x (78 + 29x + x2) = 360 Solving 78 + 29x + x2 = 360 Solving for variable 'x'. Reorder the terms: 78 + -360 + 29x + x2 = 360 + -360 Combine like terms: 78 + -360 = -282 -282 + 29x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -282 + 29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '282' to each side of the equation. -282 + 29x + 282 + x2 = 0 + 282 Reorder the terms: -282 + 282 + 29x + x2 = 0 + 282 Combine like terms: -282 + 282 = 0 0 + 29x + x2 = 0 + 282 29x + x2 = 0 + 282 Combine like terms: 0 + 282 = 282 29x + x2 = 282 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 282 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 282 + 210.25 Combine like terms: 282 + 210.25 = 492.25 210.25 + 29x + x2 = 492.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 492.25 Calculate the square root of the right side: 22.186707732 Break this problem into two subproblems by setting (x + 14.5) equal to 22.186707732 and -22.186707732.Subproblem 1
x + 14.5 = 22.186707732 Simplifying x + 14.5 = 22.186707732 Reorder the terms: 14.5 + x = 22.186707732 Solving 14.5 + x = 22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 22.186707732 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 22.186707732 + -14.5 x = 22.186707732 + -14.5 Combine like terms: 22.186707732 + -14.5 = 7.686707732 x = 7.686707732 Simplifying x = 7.686707732Subproblem 2
x + 14.5 = -22.186707732 Simplifying x + 14.5 = -22.186707732 Reorder the terms: 14.5 + x = -22.186707732 Solving 14.5 + x = -22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -22.186707732 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -22.186707732 + -14.5 x = -22.186707732 + -14.5 Combine like terms: -22.186707732 + -14.5 = -36.686707732 x = -36.686707732 Simplifying x = -36.686707732Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.686707732, -36.686707732}
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