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Simplifying x = 50 + 6x + -0.5x2 Solving x = 50 + 6x + -0.5x2 Solving for variable 'x'. Reorder the terms: -50 + x + -6x + 0.5x2 = 50 + 6x + -0.5x2 + -50 + -6x + 0.5x2 Combine like terms: x + -6x = -5x -50 + -5x + 0.5x2 = 50 + 6x + -0.5x2 + -50 + -6x + 0.5x2 Reorder the terms: -50 + -5x + 0.5x2 = 50 + -50 + 6x + -6x + -0.5x2 + 0.5x2 Combine like terms: 50 + -50 = 0 -50 + -5x + 0.5x2 = 0 + 6x + -6x + -0.5x2 + 0.5x2 -50 + -5x + 0.5x2 = 6x + -6x + -0.5x2 + 0.5x2 Combine like terms: 6x + -6x = 0 -50 + -5x + 0.5x2 = 0 + -0.5x2 + 0.5x2 -50 + -5x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -50 + -5x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -100 + -10x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -10x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -10x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -10x + x2 = 0 + 100 -10x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -10x + x2 = 100 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 100 + 25 Reorder the terms: 25 + -10x + x2 = 100 + 25 Combine like terms: 100 + 25 = 125 25 + -10x + x2 = 125 Factor a perfect square on the left side: (x + -5)(x + -5) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -5) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -5 = 11.180339887 Simplifying x + -5 = 11.180339887 Reorder the terms: -5 + x = 11.180339887 Solving -5 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + x = 11.180339887 + 5 x = 11.180339887 + 5 Combine like terms: 11.180339887 + 5 = 16.180339887 x = 16.180339887 Simplifying x = 16.180339887Subproblem 2
x + -5 = -11.180339887 Simplifying x + -5 = -11.180339887 Reorder the terms: -5 + x = -11.180339887 Solving -5 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + x = -11.180339887 + 5 x = -11.180339887 + 5 Combine like terms: -11.180339887 + 5 = -6.180339887 x = -6.180339887 Simplifying x = -6.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.180339887, -6.180339887}
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