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Simplifying 2x2 + 19x + -27 = 0 Reorder the terms: -27 + 19x + 2x2 = 0 Solving -27 + 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'. -13.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 9.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 9.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 9.5x + x2 = 0 + 13.5 9.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 9.5x + x2 = 13.5 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 = 13.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 13.5 + 22.5625 Combine like terms: 13.5 + 22.5625 = 36.0625 22.5625 + 9.5x + x2 = 36.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 36.0625 Calculate the square root of the right side: 6.005206075 Break this problem into two subproblems by setting (x + 4.75) equal to 6.005206075 and -6.005206075.Subproblem 1
x + 4.75 = 6.005206075 Simplifying x + 4.75 = 6.005206075 Reorder the terms: 4.75 + x = 6.005206075 Solving 4.75 + x = 6.005206075 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 = 6.005206075 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.005206075 + -4.75 x = 6.005206075 + -4.75 Combine like terms: 6.005206075 + -4.75 = 1.255206075 x = 1.255206075 Simplifying x = 1.255206075Subproblem 2
x + 4.75 = -6.005206075 Simplifying x + 4.75 = -6.005206075 Reorder the terms: 4.75 + x = -6.005206075 Solving 4.75 + x = -6.005206075 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 = -6.005206075 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.005206075 + -4.75 x = -6.005206075 + -4.75 Combine like terms: -6.005206075 + -4.75 = -10.755206075 x = -10.755206075 Simplifying x = -10.755206075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.255206075, -10.755206075}
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