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Simplifying 17x2 + 18x + -19 = 0 Reorder the terms: -19 + 18x + 17x2 = 0 Solving -19 + 18x + 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'. -1.117647059 + 1.058823529x + x2 = 0 Move the constant term to the right: Add '1.117647059' to each side of the equation. -1.117647059 + 1.058823529x + 1.117647059 + x2 = 0 + 1.117647059 Reorder the terms: -1.117647059 + 1.117647059 + 1.058823529x + x2 = 0 + 1.117647059 Combine like terms: -1.117647059 + 1.117647059 = 0.000000000 0.000000000 + 1.058823529x + x2 = 0 + 1.117647059 1.058823529x + x2 = 0 + 1.117647059 Combine like terms: 0 + 1.117647059 = 1.117647059 1.058823529x + x2 = 1.117647059 The x term is 1.058823529x. Take half its coefficient (0.5294117645). Square it (0.2802768164) and add it to both sides. Add '0.2802768164' to each side of the equation. 1.058823529x + 0.2802768164 + x2 = 1.117647059 + 0.2802768164 Reorder the terms: 0.2802768164 + 1.058823529x + x2 = 1.117647059 + 0.2802768164 Combine like terms: 1.117647059 + 0.2802768164 = 1.3979238754 0.2802768164 + 1.058823529x + x2 = 1.3979238754 Factor a perfect square on the left side: (x + 0.5294117645)(x + 0.5294117645) = 1.3979238754 Calculate the square root of the right side: 1.182338308 Break this problem into two subproblems by setting (x + 0.5294117645) equal to 1.182338308 and -1.182338308.Subproblem 1
x + 0.5294117645 = 1.182338308 Simplifying x + 0.5294117645 = 1.182338308 Reorder the terms: 0.5294117645 + x = 1.182338308 Solving 0.5294117645 + x = 1.182338308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5294117645' to each side of the equation. 0.5294117645 + -0.5294117645 + x = 1.182338308 + -0.5294117645 Combine like terms: 0.5294117645 + -0.5294117645 = 0.0000000000 0.0000000000 + x = 1.182338308 + -0.5294117645 x = 1.182338308 + -0.5294117645 Combine like terms: 1.182338308 + -0.5294117645 = 0.6529265435 x = 0.6529265435 Simplifying x = 0.6529265435Subproblem 2
x + 0.5294117645 = -1.182338308 Simplifying x + 0.5294117645 = -1.182338308 Reorder the terms: 0.5294117645 + x = -1.182338308 Solving 0.5294117645 + x = -1.182338308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5294117645' to each side of the equation. 0.5294117645 + -0.5294117645 + x = -1.182338308 + -0.5294117645 Combine like terms: 0.5294117645 + -0.5294117645 = 0.0000000000 0.0000000000 + x = -1.182338308 + -0.5294117645 x = -1.182338308 + -0.5294117645 Combine like terms: -1.182338308 + -0.5294117645 = -1.7117500725 x = -1.7117500725 Simplifying x = -1.7117500725Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6529265435, -1.7117500725}
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