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Simplifying 19x2 + 19x + -4 = 0 Reorder the terms: -4 + 19x + 19x2 = 0 Solving -4 + 19x + 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'. -0.2105263158 + x + x2 = 0 Move the constant term to the right: Add '0.2105263158' to each side of the equation. -0.2105263158 + x + 0.2105263158 + x2 = 0 + 0.2105263158 Reorder the terms: -0.2105263158 + 0.2105263158 + x + x2 = 0 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.2105263158 x + x2 = 0 + 0.2105263158 Combine like terms: 0 + 0.2105263158 = 0.2105263158 x + x2 = 0.2105263158 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.2105263158 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.2105263158 + 0.25 Combine like terms: 0.2105263158 + 0.25 = 0.4605263158 1.25 + x2 = 0.4605263158 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4605263158 Calculate the square root of the right side: 0.678620893 Break this problem into two subproblems by setting (x + 0.5) equal to 0.678620893 and -0.678620893.Subproblem 1
x + 0.5 = 0.678620893 Simplifying x + 0.5 = 0.678620893 Reorder the terms: 0.5 + x = 0.678620893 Solving 0.5 + x = 0.678620893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.678620893 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.678620893 + -0.5 x = 0.678620893 + -0.5 Combine like terms: 0.678620893 + -0.5 = 0.178620893 x = 0.178620893 Simplifying x = 0.178620893Subproblem 2
x + 0.5 = -0.678620893 Simplifying x + 0.5 = -0.678620893 Reorder the terms: 0.5 + x = -0.678620893 Solving 0.5 + x = -0.678620893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.678620893 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.678620893 + -0.5 x = -0.678620893 + -0.5 Combine like terms: -0.678620893 + -0.5 = -1.178620893 x = -1.178620893 Simplifying x = -1.178620893Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.178620893, -1.178620893}
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