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Simplifying 2x2 + -19x = -12 Reorder the terms: -19x + 2x2 = -12 Solving -19x + 2x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + -19x + 2x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -19x + 2x2 = 0 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 = 16.5625 22.5625 + -9.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -4.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -4.75 = 4.069705149 Simplifying x + -4.75 = 4.069705149 Reorder the terms: -4.75 + x = 4.069705149 Solving -4.75 + x = 4.069705149 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 = 4.069705149 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.069705149 + 4.75 x = 4.069705149 + 4.75 Combine like terms: 4.069705149 + 4.75 = 8.819705149 x = 8.819705149 Simplifying x = 8.819705149Subproblem 2
x + -4.75 = -4.069705149 Simplifying x + -4.75 = -4.069705149 Reorder the terms: -4.75 + x = -4.069705149 Solving -4.75 + x = -4.069705149 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 = -4.069705149 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.069705149 + 4.75 x = -4.069705149 + 4.75 Combine like terms: -4.069705149 + 4.75 = 0.680294851 x = 0.680294851 Simplifying x = 0.680294851Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.819705149, 0.680294851}
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