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Simplifying 17x2 + -14x + -20 = 0 Reorder the terms: -20 + -14x + 17x2 = 0 Solving -20 + -14x + 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 + -0.8235294118x + x2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + -0.8235294118x + 1.176470588 + x2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + -0.8235294118x + x2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + -0.8235294118x + x2 = 0 + 1.176470588 -0.8235294118x + x2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 -0.8235294118x + x2 = 1.176470588 The x term is -0.8235294118x. Take half its coefficient (-0.4117647059). Square it (0.1695501730) and add it to both sides. Add '0.1695501730' to each side of the equation. -0.8235294118x + 0.1695501730 + x2 = 1.176470588 + 0.1695501730 Reorder the terms: 0.1695501730 + -0.8235294118x + x2 = 1.176470588 + 0.1695501730 Combine like terms: 1.176470588 + 0.1695501730 = 1.346020761 0.1695501730 + -0.8235294118x + x2 = 1.346020761 Factor a perfect square on the left side: (x + -0.4117647059)(x + -0.4117647059) = 1.346020761 Calculate the square root of the right side: 1.160181348 Break this problem into two subproblems by setting (x + -0.4117647059) equal to 1.160181348 and -1.160181348.Subproblem 1
x + -0.4117647059 = 1.160181348 Simplifying x + -0.4117647059 = 1.160181348 Reorder the terms: -0.4117647059 + x = 1.160181348 Solving -0.4117647059 + x = 1.160181348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4117647059' to each side of the equation. -0.4117647059 + 0.4117647059 + x = 1.160181348 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + x = 1.160181348 + 0.4117647059 x = 1.160181348 + 0.4117647059 Combine like terms: 1.160181348 + 0.4117647059 = 1.5719460539 x = 1.5719460539 Simplifying x = 1.5719460539Subproblem 2
x + -0.4117647059 = -1.160181348 Simplifying x + -0.4117647059 = -1.160181348 Reorder the terms: -0.4117647059 + x = -1.160181348 Solving -0.4117647059 + x = -1.160181348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4117647059' to each side of the equation. -0.4117647059 + 0.4117647059 + x = -1.160181348 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + x = -1.160181348 + 0.4117647059 x = -1.160181348 + 0.4117647059 Combine like terms: -1.160181348 + 0.4117647059 = -0.7484166421 x = -0.7484166421 Simplifying x = -0.7484166421Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5719460539, -0.7484166421}
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