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Simplifying 2x2 + 19x + 1 = 0 Reorder the terms: 1 + 19x + 2x2 = 0 Solving 1 + 19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 9.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 9.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 9.5x + x2 = 0 + -0.5 9.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 9.5x + x2 = -0.5 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -0.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -0.5 + 22.5625 Combine like terms: -0.5 + 22.5625 = 22.0625 22.5625 + 9.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + 4.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + 4.75 = 4.697073557 Simplifying x + 4.75 = 4.697073557 Reorder the terms: 4.75 + x = 4.697073557 Solving 4.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 4.697073557 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.697073557 + -4.75 x = 4.697073557 + -4.75 Combine like terms: 4.697073557 + -4.75 = -0.052926443 x = -0.052926443 Simplifying x = -0.052926443Subproblem 2
x + 4.75 = -4.697073557 Simplifying x + 4.75 = -4.697073557 Reorder the terms: 4.75 + x = -4.697073557 Solving 4.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -4.697073557 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.697073557 + -4.75 x = -4.697073557 + -4.75 Combine like terms: -4.697073557 + -4.75 = -9.447073557 x = -9.447073557 Simplifying x = -9.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.052926443, -9.447073557}
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