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Simplifying x(0.5x + 4) = 160 Reorder the terms: x(4 + 0.5x) = 160 (4 * x + 0.5x * x) = 160 (4x + 0.5x2) = 160 Solving 4x + 0.5x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 4x + 0.5x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 4x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -320 + 8x + x2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + 8x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 8x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 8x + x2 = 0 + 320 8x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 8x + x2 = 320 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 = 320 + 16 Reorder the terms: 16 + 8x + x2 = 320 + 16 Combine like terms: 320 + 16 = 336 16 + 8x + x2 = 336 Factor a perfect square on the left side: (x + 4)(x + 4) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + 4) equal to 18.33030278 and -18.33030278.Subproblem 1
x + 4 = 18.33030278 Simplifying x + 4 = 18.33030278 Reorder the terms: 4 + x = 18.33030278 Solving 4 + x = 18.33030278 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 = 18.33030278 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.33030278 + -4 x = 18.33030278 + -4 Combine like terms: 18.33030278 + -4 = 14.33030278 x = 14.33030278 Simplifying x = 14.33030278Subproblem 2
x + 4 = -18.33030278 Simplifying x + 4 = -18.33030278 Reorder the terms: 4 + x = -18.33030278 Solving 4 + x = -18.33030278 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 = -18.33030278 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.33030278 + -4 x = -18.33030278 + -4 Combine like terms: -18.33030278 + -4 = -22.33030278 x = -22.33030278 Simplifying x = -22.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.33030278, -22.33030278}
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