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Simplifying x(x + 5) = 380 Reorder the terms: x(5 + x) = 380 (5 * x + x * x) = 380 (5x + x2) = 380 Solving 5x + x2 = 380 Solving for variable 'x'. Reorder the terms: -380 + 5x + x2 = 380 + -380 Combine like terms: 380 + -380 = 0 -380 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 5x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + 5x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 5x + x2 = 0 + 380 5x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 5x + x2 = 380 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 = 380 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 380 + 6.25 Combine like terms: 380 + 6.25 = 386.25 6.25 + 5x + x2 = 386.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 386.25 Calculate the square root of the right side: 19.653244007 Break this problem into two subproblems by setting (x + 2.5) equal to 19.653244007 and -19.653244007.Subproblem 1
x + 2.5 = 19.653244007 Simplifying x + 2.5 = 19.653244007 Reorder the terms: 2.5 + x = 19.653244007 Solving 2.5 + x = 19.653244007 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 = 19.653244007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 19.653244007 + -2.5 x = 19.653244007 + -2.5 Combine like terms: 19.653244007 + -2.5 = 17.153244007 x = 17.153244007 Simplifying x = 17.153244007Subproblem 2
x + 2.5 = -19.653244007 Simplifying x + 2.5 = -19.653244007 Reorder the terms: 2.5 + x = -19.653244007 Solving 2.5 + x = -19.653244007 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 = -19.653244007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -19.653244007 + -2.5 x = -19.653244007 + -2.5 Combine like terms: -19.653244007 + -2.5 = -22.153244007 x = -22.153244007 Simplifying x = -22.153244007Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.153244007, -22.153244007}
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