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Simplifying 5x + x2 = 800 Solving 5x + x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 5x + x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 5x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 5x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 5x + x2 = 0 + 800 5x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 5x + x2 = 800 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 = 800 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 800 + 6.25 Combine like terms: 800 + 6.25 = 806.25 6.25 + 5x + x2 = 806.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 806.25 Calculate the square root of the right side: 28.394541729 Break this problem into two subproblems by setting (x + 2.5) equal to 28.394541729 and -28.394541729.Subproblem 1
x + 2.5 = 28.394541729 Simplifying x + 2.5 = 28.394541729 Reorder the terms: 2.5 + x = 28.394541729 Solving 2.5 + x = 28.394541729 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 = 28.394541729 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 28.394541729 + -2.5 x = 28.394541729 + -2.5 Combine like terms: 28.394541729 + -2.5 = 25.894541729 x = 25.894541729 Simplifying x = 25.894541729Subproblem 2
x + 2.5 = -28.394541729 Simplifying x + 2.5 = -28.394541729 Reorder the terms: 2.5 + x = -28.394541729 Solving 2.5 + x = -28.394541729 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 = -28.394541729 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -28.394541729 + -2.5 x = -28.394541729 + -2.5 Combine like terms: -28.394541729 + -2.5 = -30.894541729 x = -30.894541729 Simplifying x = -30.894541729Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.894541729, -30.894541729}
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