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Simplifying x = 0.01625x2 + 0.1625x + 2.25 Reorder the terms: x = 2.25 + 0.1625x + 0.01625x2 Solving x = 2.25 + 0.1625x + 0.01625x2 Solving for variable 'x'. Reorder the terms: -2.25 + x + -0.1625x + -0.01625x2 = 2.25 + 0.1625x + 0.01625x2 + -2.25 + -0.1625x + -0.01625x2 Combine like terms: x + -0.1625x = 0.8375x -2.25 + 0.8375x + -0.01625x2 = 2.25 + 0.1625x + 0.01625x2 + -2.25 + -0.1625x + -0.01625x2 Reorder the terms: -2.25 + 0.8375x + -0.01625x2 = 2.25 + -2.25 + 0.1625x + -0.1625x + 0.01625x2 + -0.01625x2 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + 0.8375x + -0.01625x2 = 0.00 + 0.1625x + -0.1625x + 0.01625x2 + -0.01625x2 -2.25 + 0.8375x + -0.01625x2 = 0.1625x + -0.1625x + 0.01625x2 + -0.01625x2 Combine like terms: 0.1625x + -0.1625x = 0.0000 -2.25 + 0.8375x + -0.01625x2 = 0.0000 + 0.01625x2 + -0.01625x2 -2.25 + 0.8375x + -0.01625x2 = 0.01625x2 + -0.01625x2 Combine like terms: 0.01625x2 + -0.01625x2 = 0.00000 -2.25 + 0.8375x + -0.01625x2 = 0.00000 Begin completing the square. Divide all terms by -0.01625 the coefficient of the squared term: Divide each side by '-0.01625'. 138.4615385 + -51.53846154x + x2 = 0 Move the constant term to the right: Add '-138.4615385' to each side of the equation. 138.4615385 + -51.53846154x + -138.4615385 + x2 = 0 + -138.4615385 Reorder the terms: 138.4615385 + -138.4615385 + -51.53846154x + x2 = 0 + -138.4615385 Combine like terms: 138.4615385 + -138.4615385 = 0.0000000 0.0000000 + -51.53846154x + x2 = 0 + -138.4615385 -51.53846154x + x2 = 0 + -138.4615385 Combine like terms: 0 + -138.4615385 = -138.4615385 -51.53846154x + x2 = -138.4615385 The x term is -51.53846154x. Take half its coefficient (-25.76923077). Square it (664.0532545) and add it to both sides. Add '664.0532545' to each side of the equation. -51.53846154x + 664.0532545 + x2 = -138.4615385 + 664.0532545 Reorder the terms: 664.0532545 + -51.53846154x + x2 = -138.4615385 + 664.0532545 Combine like terms: -138.4615385 + 664.0532545 = 525.591716 664.0532545 + -51.53846154x + x2 = 525.591716 Factor a perfect square on the left side: (x + -25.76923077)(x + -25.76923077) = 525.591716 Calculate the square root of the right side: 22.92578714 Break this problem into two subproblems by setting (x + -25.76923077) equal to 22.92578714 and -22.92578714.Subproblem 1
x + -25.76923077 = 22.92578714 Simplifying x + -25.76923077 = 22.92578714 Reorder the terms: -25.76923077 + x = 22.92578714 Solving -25.76923077 + x = 22.92578714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.76923077' to each side of the equation. -25.76923077 + 25.76923077 + x = 22.92578714 + 25.76923077 Combine like terms: -25.76923077 + 25.76923077 = 0.00000000 0.00000000 + x = 22.92578714 + 25.76923077 x = 22.92578714 + 25.76923077 Combine like terms: 22.92578714 + 25.76923077 = 48.69501791 x = 48.69501791 Simplifying x = 48.69501791Subproblem 2
x + -25.76923077 = -22.92578714 Simplifying x + -25.76923077 = -22.92578714 Reorder the terms: -25.76923077 + x = -22.92578714 Solving -25.76923077 + x = -22.92578714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.76923077' to each side of the equation. -25.76923077 + 25.76923077 + x = -22.92578714 + 25.76923077 Combine like terms: -25.76923077 + 25.76923077 = 0.00000000 0.00000000 + x = -22.92578714 + 25.76923077 x = -22.92578714 + 25.76923077 Combine like terms: -22.92578714 + 25.76923077 = 2.84344363 x = 2.84344363 Simplifying x = 2.84344363Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.69501791, 2.84344363}
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