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Simplifying (x + 5)(x + 5) = 1280 Reorder the terms: (5 + x)(x + 5) = 1280 Reorder the terms: (5 + x)(5 + x) = 1280 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 1280 ((5 * 5 + x * 5) + x(5 + x)) = 1280 ((25 + 5x) + x(5 + x)) = 1280 (25 + 5x + (5 * x + x * x)) = 1280 (25 + 5x + (5x + x2)) = 1280 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 1280 Solving 25 + 10x + x2 = 1280 Solving for variable 'x'. Reorder the terms: 25 + -1280 + 10x + x2 = 1280 + -1280 Combine like terms: 25 + -1280 = -1255 -1255 + 10x + x2 = 1280 + -1280 Combine like terms: 1280 + -1280 = 0 -1255 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1255' to each side of the equation. -1255 + 10x + 1255 + x2 = 0 + 1255 Reorder the terms: -1255 + 1255 + 10x + x2 = 0 + 1255 Combine like terms: -1255 + 1255 = 0 0 + 10x + x2 = 0 + 1255 10x + x2 = 0 + 1255 Combine like terms: 0 + 1255 = 1255 10x + x2 = 1255 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 = 1255 + 25 Reorder the terms: 25 + 10x + x2 = 1255 + 25 Combine like terms: 1255 + 25 = 1280 25 + 10x + x2 = 1280 Factor a perfect square on the left side: (x + 5)(x + 5) = 1280 Calculate the square root of the right side: 35.77708764 Break this problem into two subproblems by setting (x + 5) equal to 35.77708764 and -35.77708764.Subproblem 1
x + 5 = 35.77708764 Simplifying x + 5 = 35.77708764 Reorder the terms: 5 + x = 35.77708764 Solving 5 + x = 35.77708764 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 = 35.77708764 + -5 Combine like terms: 5 + -5 = 0 0 + x = 35.77708764 + -5 x = 35.77708764 + -5 Combine like terms: 35.77708764 + -5 = 30.77708764 x = 30.77708764 Simplifying x = 30.77708764Subproblem 2
x + 5 = -35.77708764 Simplifying x + 5 = -35.77708764 Reorder the terms: 5 + x = -35.77708764 Solving 5 + x = -35.77708764 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 = -35.77708764 + -5 Combine like terms: 5 + -5 = 0 0 + x = -35.77708764 + -5 x = -35.77708764 + -5 Combine like terms: -35.77708764 + -5 = -40.77708764 x = -40.77708764 Simplifying x = -40.77708764Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.77708764, -40.77708764}
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