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Simplifying 30.40x2 + -90.6x + 41.96 = 0 Reorder the terms: 41.96 + -90.6x + 30.40x2 = 0 Solving 41.96 + -90.6x + 30.40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30.40 the coefficient of the squared term: Divide each side by '30.40'. 1.380263158 + -2.980263158x + x2 = 0 Move the constant term to the right: Add '-1.380263158' to each side of the equation. 1.380263158 + -2.980263158x + -1.380263158 + x2 = 0 + -1.380263158 Reorder the terms: 1.380263158 + -1.380263158 + -2.980263158x + x2 = 0 + -1.380263158 Combine like terms: 1.380263158 + -1.380263158 = 0.000000000 0.000000000 + -2.980263158x + x2 = 0 + -1.380263158 -2.980263158x + x2 = 0 + -1.380263158 Combine like terms: 0 + -1.380263158 = -1.380263158 -2.980263158x + x2 = -1.380263158 The x term is -2.980263158x. Take half its coefficient (-1.490131579). Square it (2.220492123) and add it to both sides. Add '2.220492123' to each side of the equation. -2.980263158x + 2.220492123 + x2 = -1.380263158 + 2.220492123 Reorder the terms: 2.220492123 + -2.980263158x + x2 = -1.380263158 + 2.220492123 Combine like terms: -1.380263158 + 2.220492123 = 0.840228965 2.220492123 + -2.980263158x + x2 = 0.840228965 Factor a perfect square on the left side: (x + -1.490131579)(x + -1.490131579) = 0.840228965 Calculate the square root of the right side: 0.916640041 Break this problem into two subproblems by setting (x + -1.490131579) equal to 0.916640041 and -0.916640041.Subproblem 1
x + -1.490131579 = 0.916640041 Simplifying x + -1.490131579 = 0.916640041 Reorder the terms: -1.490131579 + x = 0.916640041 Solving -1.490131579 + x = 0.916640041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.490131579' to each side of the equation. -1.490131579 + 1.490131579 + x = 0.916640041 + 1.490131579 Combine like terms: -1.490131579 + 1.490131579 = 0.000000000 0.000000000 + x = 0.916640041 + 1.490131579 x = 0.916640041 + 1.490131579 Combine like terms: 0.916640041 + 1.490131579 = 2.40677162 x = 2.40677162 Simplifying x = 2.40677162Subproblem 2
x + -1.490131579 = -0.916640041 Simplifying x + -1.490131579 = -0.916640041 Reorder the terms: -1.490131579 + x = -0.916640041 Solving -1.490131579 + x = -0.916640041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.490131579' to each side of the equation. -1.490131579 + 1.490131579 + x = -0.916640041 + 1.490131579 Combine like terms: -1.490131579 + 1.490131579 = 0.000000000 0.000000000 + x = -0.916640041 + 1.490131579 x = -0.916640041 + 1.490131579 Combine like terms: -0.916640041 + 1.490131579 = 0.573491538 x = 0.573491538 Simplifying x = 0.573491538Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.40677162, 0.573491538}
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