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Simplifying 4x2 + 19x + 2 = 0 Reorder the terms: 2 + 19x + 4x2 = 0 Solving 2 + 19x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 4.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4.75x + x2 = 0 + -0.5 4.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4.75x + x2 = -0.5 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = -0.5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = -0.5 + 5.640625 Combine like terms: -0.5 + 5.640625 = 5.140625 5.640625 + 4.75x + x2 = 5.140625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + 2.375) equal to 2.267294643 and -2.267294643.Subproblem 1
x + 2.375 = 2.267294643 Simplifying x + 2.375 = 2.267294643 Reorder the terms: 2.375 + x = 2.267294643 Solving 2.375 + x = 2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.267294643 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.267294643 + -2.375 x = 2.267294643 + -2.375 Combine like terms: 2.267294643 + -2.375 = -0.107705357 x = -0.107705357 Simplifying x = -0.107705357Subproblem 2
x + 2.375 = -2.267294643 Simplifying x + 2.375 = -2.267294643 Reorder the terms: 2.375 + x = -2.267294643 Solving 2.375 + x = -2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.267294643 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.267294643 + -2.375 x = -2.267294643 + -2.375 Combine like terms: -2.267294643 + -2.375 = -4.642294643 x = -4.642294643 Simplifying x = -4.642294643Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.107705357, -4.642294643}
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