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Simplifying 19x + 2x2 + 38 = 0 Reorder the terms: 38 + 19x + 2x2 = 0 Solving 38 + 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'. 19 + 9.5x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + 9.5x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 9.5x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 9.5x + x2 = 0 + -19 9.5x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 9.5x + x2 = -19 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 = -19 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -19 + 22.5625 Combine like terms: -19 + 22.5625 = 3.5625 22.5625 + 9.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 4.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 4.75 = 1.887458609 Simplifying x + 4.75 = 1.887458609 Reorder the terms: 4.75 + x = 1.887458609 Solving 4.75 + x = 1.887458609 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 = 1.887458609 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 1.887458609 + -4.75 x = 1.887458609 + -4.75 Combine like terms: 1.887458609 + -4.75 = -2.862541391 x = -2.862541391 Simplifying x = -2.862541391Subproblem 2
x + 4.75 = -1.887458609 Simplifying x + 4.75 = -1.887458609 Reorder the terms: 4.75 + x = -1.887458609 Solving 4.75 + x = -1.887458609 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 = -1.887458609 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -1.887458609 + -4.75 x = -1.887458609 + -4.75 Combine like terms: -1.887458609 + -4.75 = -6.637458609 x = -6.637458609 Simplifying x = -6.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.862541391, -6.637458609}
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