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Simplifying x(x + 5) = 160 Reorder the terms: x(5 + x) = 160 (5 * x + x * x) = 160 (5x + x2) = 160 Solving 5x + x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 5x + x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 5x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 5x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 5x + x2 = 0 + 160 5x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 5x + x2 = 160 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 = 160 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 160 + 6.25 Combine like terms: 160 + 6.25 = 166.25 6.25 + 5x + x2 = 166.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (x + 2.5) equal to 12.893796958 and -12.893796958.Subproblem 1
x + 2.5 = 12.893796958 Simplifying x + 2.5 = 12.893796958 Reorder the terms: 2.5 + x = 12.893796958 Solving 2.5 + x = 12.893796958 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 = 12.893796958 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.893796958 + -2.5 x = 12.893796958 + -2.5 Combine like terms: 12.893796958 + -2.5 = 10.393796958 x = 10.393796958 Simplifying x = 10.393796958Subproblem 2
x + 2.5 = -12.893796958 Simplifying x + 2.5 = -12.893796958 Reorder the terms: 2.5 + x = -12.893796958 Solving 2.5 + x = -12.893796958 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 = -12.893796958 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.893796958 + -2.5 x = -12.893796958 + -2.5 Combine like terms: -12.893796958 + -2.5 = -15.393796958 x = -15.393796958 Simplifying x = -15.393796958Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.393796958, -15.393796958}
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