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Simplifying 2x2 + 19x + 3 = 0 Reorder the terms: 3 + 19x + 2x2 = 0 Solving 3 + 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'. 1.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 9.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 9.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 9.5x + x2 = 0 + -1.5 9.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 9.5x + x2 = -1.5 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 = -1.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -1.5 + 22.5625 Combine like terms: -1.5 + 22.5625 = 21.0625 22.5625 + 9.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + 4.75) equal to 4.589389938 and -4.589389938.Subproblem 1
x + 4.75 = 4.589389938 Simplifying x + 4.75 = 4.589389938 Reorder the terms: 4.75 + x = 4.589389938 Solving 4.75 + x = 4.589389938 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 = 4.589389938 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 4.589389938 + -4.75 x = 4.589389938 + -4.75 Combine like terms: 4.589389938 + -4.75 = -0.160610062 x = -0.160610062 Simplifying x = -0.160610062Subproblem 2
x + 4.75 = -4.589389938 Simplifying x + 4.75 = -4.589389938 Reorder the terms: 4.75 + x = -4.589389938 Solving 4.75 + x = -4.589389938 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 = -4.589389938 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -4.589389938 + -4.75 x = -4.589389938 + -4.75 Combine like terms: -4.589389938 + -4.75 = -9.339389938 x = -9.339389938 Simplifying x = -9.339389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.160610062, -9.339389938}
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