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Simplifying x2 + 8x = 500 Reorder the terms: 8x + x2 = 500 Solving 8x + x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 8x + x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 8x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 8x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 8x + x2 = 0 + 500 8x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 8x + x2 = 500 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 500 + 16 Reorder the terms: 16 + 8x + x2 = 500 + 16 Combine like terms: 500 + 16 = 516 16 + 8x + x2 = 516 Factor a perfect square on the left side: (x + 4)(x + 4) = 516 Calculate the square root of the right side: 22.715633383 Break this problem into two subproblems by setting (x + 4) equal to 22.715633383 and -22.715633383.Subproblem 1
x + 4 = 22.715633383 Simplifying x + 4 = 22.715633383 Reorder the terms: 4 + x = 22.715633383 Solving 4 + x = 22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 22.715633383 + -4 Combine like terms: 4 + -4 = 0 0 + x = 22.715633383 + -4 x = 22.715633383 + -4 Combine like terms: 22.715633383 + -4 = 18.715633383 x = 18.715633383 Simplifying x = 18.715633383Subproblem 2
x + 4 = -22.715633383 Simplifying x + 4 = -22.715633383 Reorder the terms: 4 + x = -22.715633383 Solving 4 + x = -22.715633383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -22.715633383 + -4 Combine like terms: 4 + -4 = 0 0 + x = -22.715633383 + -4 x = -22.715633383 + -4 Combine like terms: -22.715633383 + -4 = -26.715633383 x = -26.715633383 Simplifying x = -26.715633383Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.715633383, -26.715633383}
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