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Simplifying 2.8 = 0.02041x(28 + -1x) 2.8 = (28 * 0.02041x + -1x * 0.02041x) 2.8 = (0.57148x + -0.02041x2) Solving 2.8 = 0.57148x + -0.02041x2 Solving for variable 'x'. Reorder the terms: 2.8 + -0.57148x + 0.02041x2 = 0.57148x + -0.57148x + -0.02041x2 + 0.02041x2 Combine like terms: 0.57148x + -0.57148x = 0.00000 2.8 + -0.57148x + 0.02041x2 = 0.00000 + -0.02041x2 + 0.02041x2 2.8 + -0.57148x + 0.02041x2 = -0.02041x2 + 0.02041x2 Combine like terms: -0.02041x2 + 0.02041x2 = 0.00000 2.8 + -0.57148x + 0.02041x2 = 0.00000 Begin completing the square. Divide all terms by 0.02041 the coefficient of the squared term: Divide each side by '0.02041'. 137.1876531 + -28x + x2 = 0 Move the constant term to the right: Add '-137.1876531' to each side of the equation. 137.1876531 + -28x + -137.1876531 + x2 = 0 + -137.1876531 Reorder the terms: 137.1876531 + -137.1876531 + -28x + x2 = 0 + -137.1876531 Combine like terms: 137.1876531 + -137.1876531 = 0.0000000 0.0000000 + -28x + x2 = 0 + -137.1876531 -28x + x2 = 0 + -137.1876531 Combine like terms: 0 + -137.1876531 = -137.1876531 -28x + x2 = -137.1876531 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -137.1876531 + 196 Reorder the terms: 196 + -28x + x2 = -137.1876531 + 196 Combine like terms: -137.1876531 + 196 = 58.8123469 196 + -28x + x2 = 58.8123469 Factor a perfect square on the left side: (x + -14)(x + -14) = 58.8123469 Calculate the square root of the right side: 7.668920843 Break this problem into two subproblems by setting (x + -14) equal to 7.668920843 and -7.668920843.Subproblem 1
x + -14 = 7.668920843 Simplifying x + -14 = 7.668920843 Reorder the terms: -14 + x = 7.668920843 Solving -14 + x = 7.668920843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 7.668920843 + 14 Combine like terms: -14 + 14 = 0 0 + x = 7.668920843 + 14 x = 7.668920843 + 14 Combine like terms: 7.668920843 + 14 = 21.668920843 x = 21.668920843 Simplifying x = 21.668920843Subproblem 2
x + -14 = -7.668920843 Simplifying x + -14 = -7.668920843 Reorder the terms: -14 + x = -7.668920843 Solving -14 + x = -7.668920843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -7.668920843 + 14 Combine like terms: -14 + 14 = 0 0 + x = -7.668920843 + 14 x = -7.668920843 + 14 Combine like terms: -7.668920843 + 14 = 6.331079157 x = 6.331079157 Simplifying x = 6.331079157Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.668920843, 6.331079157}
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