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Simplifying 2x2 + -19x + 22 = 0 Reorder the terms: 22 + -19x + 2x2 = 0 Solving 22 + -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'. 11 + -9.5x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -9.5x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -9.5x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9.5x + x2 = 0 + -11 -9.5x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -9.5x + x2 = -11 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 = -11 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -11 + 22.5625 Combine like terms: -11 + 22.5625 = 11.5625 22.5625 + -9.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -4.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -4.75 = 3.400367627 Simplifying x + -4.75 = 3.400367627 Reorder the terms: -4.75 + x = 3.400367627 Solving -4.75 + x = 3.400367627 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 = 3.400367627 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.400367627 + 4.75 x = 3.400367627 + 4.75 Combine like terms: 3.400367627 + 4.75 = 8.150367627 x = 8.150367627 Simplifying x = 8.150367627Subproblem 2
x + -4.75 = -3.400367627 Simplifying x + -4.75 = -3.400367627 Reorder the terms: -4.75 + x = -3.400367627 Solving -4.75 + x = -3.400367627 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 = -3.400367627 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.400367627 + 4.75 x = -3.400367627 + 4.75 Combine like terms: -3.400367627 + 4.75 = 1.349632373 x = 1.349632373 Simplifying x = 1.349632373Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.150367627, 1.349632373}
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