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Simplifying 19x2 + -8x + -20 = 0 Reorder the terms: -20 + -8x + 19x2 = 0 Solving -20 + -8x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -1.052631579 + -0.4210526316x + x2 = 0 Move the constant term to the right: Add '1.052631579' to each side of the equation. -1.052631579 + -0.4210526316x + 1.052631579 + x2 = 0 + 1.052631579 Reorder the terms: -1.052631579 + 1.052631579 + -0.4210526316x + x2 = 0 + 1.052631579 Combine like terms: -1.052631579 + 1.052631579 = 0.000000000 0.000000000 + -0.4210526316x + x2 = 0 + 1.052631579 -0.4210526316x + x2 = 0 + 1.052631579 Combine like terms: 0 + 1.052631579 = 1.052631579 -0.4210526316x + x2 = 1.052631579 The x term is -0.4210526316x. Take half its coefficient (-0.2105263158). Square it (0.04432132964) and add it to both sides. Add '0.04432132964' to each side of the equation. -0.4210526316x + 0.04432132964 + x2 = 1.052631579 + 0.04432132964 Reorder the terms: 0.04432132964 + -0.4210526316x + x2 = 1.052631579 + 0.04432132964 Combine like terms: 1.052631579 + 0.04432132964 = 1.09695290864 0.04432132964 + -0.4210526316x + x2 = 1.09695290864 Factor a perfect square on the left side: (x + -0.2105263158)(x + -0.2105263158) = 1.09695290864 Calculate the square root of the right side: 1.047355197 Break this problem into two subproblems by setting (x + -0.2105263158) equal to 1.047355197 and -1.047355197.Subproblem 1
x + -0.2105263158 = 1.047355197 Simplifying x + -0.2105263158 = 1.047355197 Reorder the terms: -0.2105263158 + x = 1.047355197 Solving -0.2105263158 + x = 1.047355197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2105263158' to each side of the equation. -0.2105263158 + 0.2105263158 + x = 1.047355197 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + x = 1.047355197 + 0.2105263158 x = 1.047355197 + 0.2105263158 Combine like terms: 1.047355197 + 0.2105263158 = 1.2578815128 x = 1.2578815128 Simplifying x = 1.2578815128Subproblem 2
x + -0.2105263158 = -1.047355197 Simplifying x + -0.2105263158 = -1.047355197 Reorder the terms: -0.2105263158 + x = -1.047355197 Solving -0.2105263158 + x = -1.047355197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2105263158' to each side of the equation. -0.2105263158 + 0.2105263158 + x = -1.047355197 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + x = -1.047355197 + 0.2105263158 x = -1.047355197 + 0.2105263158 Combine like terms: -1.047355197 + 0.2105263158 = -0.8368288812 x = -0.8368288812 Simplifying x = -0.8368288812Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2578815128, -0.8368288812}
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