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Simplifying (x + 5)(x) = 400 Reorder the terms: (5 + x)(x) = 400 Reorder the terms for easier multiplication: x(5 + x) = 400 (5 * x + x * x) = 400 (5x + x2) = 400 Solving 5x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 5x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 5x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 5x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 5x + x2 = 0 + 400 5x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 5x + x2 = 400 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 400 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 400 + 6.25 Combine like terms: 400 + 6.25 = 406.25 6.25 + 5x + x2 = 406.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 406.25 Calculate the square root of the right side: 20.155644371 Break this problem into two subproblems by setting (x + 2.5) equal to 20.155644371 and -20.155644371.Subproblem 1
x + 2.5 = 20.155644371 Simplifying x + 2.5 = 20.155644371 Reorder the terms: 2.5 + x = 20.155644371 Solving 2.5 + x = 20.155644371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 20.155644371 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 20.155644371 + -2.5 x = 20.155644371 + -2.5 Combine like terms: 20.155644371 + -2.5 = 17.655644371 x = 17.655644371 Simplifying x = 17.655644371Subproblem 2
x + 2.5 = -20.155644371 Simplifying x + 2.5 = -20.155644371 Reorder the terms: 2.5 + x = -20.155644371 Solving 2.5 + x = -20.155644371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -20.155644371 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -20.155644371 + -2.5 x = -20.155644371 + -2.5 Combine like terms: -20.155644371 + -2.5 = -22.655644371 x = -22.655644371 Simplifying x = -22.655644371Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.655644371, -22.655644371}
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