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Simplifying 0.18x2 + -1.6x + 3.1 = 0 Reorder the terms: 3.1 + -1.6x + 0.18x2 = 0 Solving 3.1 + -1.6x + 0.18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.18 the coefficient of the squared term: Divide each side by '0.18'. 17.22222222 + -8.888888889x + x2 = 0 Move the constant term to the right: Add '-17.22222222' to each side of the equation. 17.22222222 + -8.888888889x + -17.22222222 + x2 = 0 + -17.22222222 Reorder the terms: 17.22222222 + -17.22222222 + -8.888888889x + x2 = 0 + -17.22222222 Combine like terms: 17.22222222 + -17.22222222 = 0.00000000 0.00000000 + -8.888888889x + x2 = 0 + -17.22222222 -8.888888889x + x2 = 0 + -17.22222222 Combine like terms: 0 + -17.22222222 = -17.22222222 -8.888888889x + x2 = -17.22222222 The x term is -8.888888889x. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889x + 19.75308642 + x2 = -17.22222222 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889x + x2 = -17.22222222 + 19.75308642 Combine like terms: -17.22222222 + 19.75308642 = 2.5308642 19.75308642 + -8.888888889x + x2 = 2.5308642 Factor a perfect square on the left side: (x + -4.444444445)(x + -4.444444445) = 2.5308642 Calculate the square root of the right side: 1.590869008 Break this problem into two subproblems by setting (x + -4.444444445) equal to 1.590869008 and -1.590869008.Subproblem 1
x + -4.444444445 = 1.590869008 Simplifying x + -4.444444445 = 1.590869008 Reorder the terms: -4.444444445 + x = 1.590869008 Solving -4.444444445 + x = 1.590869008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = 1.590869008 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = 1.590869008 + 4.444444445 x = 1.590869008 + 4.444444445 Combine like terms: 1.590869008 + 4.444444445 = 6.035313453 x = 6.035313453 Simplifying x = 6.035313453Subproblem 2
x + -4.444444445 = -1.590869008 Simplifying x + -4.444444445 = -1.590869008 Reorder the terms: -4.444444445 + x = -1.590869008 Solving -4.444444445 + x = -1.590869008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = -1.590869008 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = -1.590869008 + 4.444444445 x = -1.590869008 + 4.444444445 Combine like terms: -1.590869008 + 4.444444445 = 2.853575437 x = 2.853575437 Simplifying x = 2.853575437Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.035313453, 2.853575437}
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