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Simplifying 2x2 + -19x + -12 = 0 Reorder the terms: -12 + -19x + 2x2 = 0 Solving -12 + -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'. -6 + -9.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -9.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -9.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -9.5x + x2 = 0 + 6 -9.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -9.5x + x2 = 6 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 = 6 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 6 + 22.5625 Combine like terms: 6 + 22.5625 = 28.5625 22.5625 + -9.5x + x2 = 28.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (x + -4.75) equal to 5.344389582 and -5.344389582.Subproblem 1
x + -4.75 = 5.344389582 Simplifying x + -4.75 = 5.344389582 Reorder the terms: -4.75 + x = 5.344389582 Solving -4.75 + x = 5.344389582 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 = 5.344389582 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.344389582 + 4.75 x = 5.344389582 + 4.75 Combine like terms: 5.344389582 + 4.75 = 10.094389582 x = 10.094389582 Simplifying x = 10.094389582Subproblem 2
x + -4.75 = -5.344389582 Simplifying x + -4.75 = -5.344389582 Reorder the terms: -4.75 + x = -5.344389582 Solving -4.75 + x = -5.344389582 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 = -5.344389582 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.344389582 + 4.75 x = -5.344389582 + 4.75 Combine like terms: -5.344389582 + 4.75 = -0.594389582 x = -0.594389582 Simplifying x = -0.594389582Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.094389582, -0.594389582}
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