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Simplifying -9x2 + -17x + 20 = 0 Reorder the terms: 20 + -17x + -9x2 = 0 Solving 20 + -17x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.222222222 + 1.888888889x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.888888889x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.888888889x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.888888889x + x2 = 0 + 2.222222222 1.888888889x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.888888889x + x2 = 2.222222222 The x term is 1.888888889x. Take half its coefficient (0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. 1.888888889x + 0.8919753087 + x2 = 2.222222222 + 0.8919753087 Reorder the terms: 0.8919753087 + 1.888888889x + x2 = 2.222222222 + 0.8919753087 Combine like terms: 2.222222222 + 0.8919753087 = 3.1141975307 0.8919753087 + 1.888888889x + x2 = 3.1141975307 Factor a perfect square on the left side: (x + 0.9444444445)(x + 0.9444444445) = 3.1141975307 Calculate the square root of the right side: 1.764708908 Break this problem into two subproblems by setting (x + 0.9444444445) equal to 1.764708908 and -1.764708908.Subproblem 1
x + 0.9444444445 = 1.764708908 Simplifying x + 0.9444444445 = 1.764708908 Reorder the terms: 0.9444444445 + x = 1.764708908 Solving 0.9444444445 + x = 1.764708908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 1.764708908 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 1.764708908 + -0.9444444445 x = 1.764708908 + -0.9444444445 Combine like terms: 1.764708908 + -0.9444444445 = 0.8202644635 x = 0.8202644635 Simplifying x = 0.8202644635Subproblem 2
x + 0.9444444445 = -1.764708908 Simplifying x + 0.9444444445 = -1.764708908 Reorder the terms: 0.9444444445 + x = -1.764708908 Solving 0.9444444445 + x = -1.764708908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -1.764708908 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -1.764708908 + -0.9444444445 x = -1.764708908 + -0.9444444445 Combine like terms: -1.764708908 + -0.9444444445 = -2.7091533525 x = -2.7091533525 Simplifying x = -2.7091533525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8202644635, -2.7091533525}
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