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Simplifying 17x2 + -49x + 20 = 0 Reorder the terms: 20 + -49x + 17x2 = 0 Solving 20 + -49x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1.176470588 + -2.882352941x + x2 = 0 Move the constant term to the right: Add '-1.176470588' to each side of the equation. 1.176470588 + -2.882352941x + -1.176470588 + x2 = 0 + -1.176470588 Reorder the terms: 1.176470588 + -1.176470588 + -2.882352941x + x2 = 0 + -1.176470588 Combine like terms: 1.176470588 + -1.176470588 = 0.000000000 0.000000000 + -2.882352941x + x2 = 0 + -1.176470588 -2.882352941x + x2 = 0 + -1.176470588 Combine like terms: 0 + -1.176470588 = -1.176470588 -2.882352941x + x2 = -1.176470588 The x term is -2.882352941x. Take half its coefficient (-1.441176471). Square it (2.076989621) and add it to both sides. Add '2.076989621' to each side of the equation. -2.882352941x + 2.076989621 + x2 = -1.176470588 + 2.076989621 Reorder the terms: 2.076989621 + -2.882352941x + x2 = -1.176470588 + 2.076989621 Combine like terms: -1.176470588 + 2.076989621 = 0.900519033 2.076989621 + -2.882352941x + x2 = 0.900519033 Factor a perfect square on the left side: (x + -1.441176471)(x + -1.441176471) = 0.900519033 Calculate the square root of the right side: 0.948956813 Break this problem into two subproblems by setting (x + -1.441176471) equal to 0.948956813 and -0.948956813.Subproblem 1
x + -1.441176471 = 0.948956813 Simplifying x + -1.441176471 = 0.948956813 Reorder the terms: -1.441176471 + x = 0.948956813 Solving -1.441176471 + x = 0.948956813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.441176471' to each side of the equation. -1.441176471 + 1.441176471 + x = 0.948956813 + 1.441176471 Combine like terms: -1.441176471 + 1.441176471 = 0.000000000 0.000000000 + x = 0.948956813 + 1.441176471 x = 0.948956813 + 1.441176471 Combine like terms: 0.948956813 + 1.441176471 = 2.390133284 x = 2.390133284 Simplifying x = 2.390133284Subproblem 2
x + -1.441176471 = -0.948956813 Simplifying x + -1.441176471 = -0.948956813 Reorder the terms: -1.441176471 + x = -0.948956813 Solving -1.441176471 + x = -0.948956813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.441176471' to each side of the equation. -1.441176471 + 1.441176471 + x = -0.948956813 + 1.441176471 Combine like terms: -1.441176471 + 1.441176471 = 0.000000000 0.000000000 + x = -0.948956813 + 1.441176471 x = -0.948956813 + 1.441176471 Combine like terms: -0.948956813 + 1.441176471 = 0.492219658 x = 0.492219658 Simplifying x = 0.492219658Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.390133284, 0.492219658}
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