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Simplifying 0 = 16.5x2 + -64.5x + 41.5 Reorder the terms: 0 = 41.5 + -64.5x + 16.5x2 Solving 0 = 41.5 + -64.5x + 16.5x2 Solving for variable 'x'. Combine like terms: 0 + -41.5 = -41.5 -41.5 + 64.5x + -16.5x2 = 41.5 + -64.5x + 16.5x2 + -41.5 + 64.5x + -16.5x2 Reorder the terms: -41.5 + 64.5x + -16.5x2 = 41.5 + -41.5 + -64.5x + 64.5x + 16.5x2 + -16.5x2 Combine like terms: 41.5 + -41.5 = 0.0 -41.5 + 64.5x + -16.5x2 = 0.0 + -64.5x + 64.5x + 16.5x2 + -16.5x2 -41.5 + 64.5x + -16.5x2 = -64.5x + 64.5x + 16.5x2 + -16.5x2 Combine like terms: -64.5x + 64.5x = 0.0 -41.5 + 64.5x + -16.5x2 = 0.0 + 16.5x2 + -16.5x2 -41.5 + 64.5x + -16.5x2 = 16.5x2 + -16.5x2 Combine like terms: 16.5x2 + -16.5x2 = 0.0 -41.5 + 64.5x + -16.5x2 = 0.0 Begin completing the square. Divide all terms by -16.5 the coefficient of the squared term: Divide each side by '-16.5'. 2.515151515 + -3.909090909x + x2 = 0 Move the constant term to the right: Add '-2.515151515' to each side of the equation. 2.515151515 + -3.909090909x + -2.515151515 + x2 = 0 + -2.515151515 Reorder the terms: 2.515151515 + -2.515151515 + -3.909090909x + x2 = 0 + -2.515151515 Combine like terms: 2.515151515 + -2.515151515 = 0.000000000 0.000000000 + -3.909090909x + x2 = 0 + -2.515151515 -3.909090909x + x2 = 0 + -2.515151515 Combine like terms: 0 + -2.515151515 = -2.515151515 -3.909090909x + x2 = -2.515151515 The x term is -3.909090909x. Take half its coefficient (-1.954545455). Square it (3.820247936) and add it to both sides. Add '3.820247936' to each side of the equation. -3.909090909x + 3.820247936 + x2 = -2.515151515 + 3.820247936 Reorder the terms: 3.820247936 + -3.909090909x + x2 = -2.515151515 + 3.820247936 Combine like terms: -2.515151515 + 3.820247936 = 1.305096421 3.820247936 + -3.909090909x + x2 = 1.305096421 Factor a perfect square on the left side: (x + -1.954545455)(x + -1.954545455) = 1.305096421 Calculate the square root of the right side: 1.142408167 Break this problem into two subproblems by setting (x + -1.954545455) equal to 1.142408167 and -1.142408167.Subproblem 1
x + -1.954545455 = 1.142408167 Simplifying x + -1.954545455 = 1.142408167 Reorder the terms: -1.954545455 + x = 1.142408167 Solving -1.954545455 + x = 1.142408167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.954545455' to each side of the equation. -1.954545455 + 1.954545455 + x = 1.142408167 + 1.954545455 Combine like terms: -1.954545455 + 1.954545455 = 0.000000000 0.000000000 + x = 1.142408167 + 1.954545455 x = 1.142408167 + 1.954545455 Combine like terms: 1.142408167 + 1.954545455 = 3.096953622 x = 3.096953622 Simplifying x = 3.096953622Subproblem 2
x + -1.954545455 = -1.142408167 Simplifying x + -1.954545455 = -1.142408167 Reorder the terms: -1.954545455 + x = -1.142408167 Solving -1.954545455 + x = -1.142408167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.954545455' to each side of the equation. -1.954545455 + 1.954545455 + x = -1.142408167 + 1.954545455 Combine like terms: -1.954545455 + 1.954545455 = 0.000000000 0.000000000 + x = -1.142408167 + 1.954545455 x = -1.142408167 + 1.954545455 Combine like terms: -1.142408167 + 1.954545455 = 0.812137288 x = 0.812137288 Simplifying x = 0.812137288Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.096953622, 0.812137288}
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