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Simplifying 5x2 + -20x + 19 = 0 Reorder the terms: 19 + -20x + 5x2 = 0 Solving 19 + -20x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.8 + -4x + x2 = 0 Move the constant term to the right: Add '-3.8' to each side of the equation. 3.8 + -4x + -3.8 + x2 = 0 + -3.8 Reorder the terms: 3.8 + -3.8 + -4x + x2 = 0 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + -4x + x2 = 0 + -3.8 -4x + x2 = 0 + -3.8 Combine like terms: 0 + -3.8 = -3.8 -4x + x2 = -3.8 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.8 + 4 Reorder the terms: 4 + -4x + x2 = -3.8 + 4 Combine like terms: -3.8 + 4 = 0.2 4 + -4x + x2 = 0.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + -2) equal to 0.447213596 and -0.447213596.Subproblem 1
x + -2 = 0.447213596 Simplifying x + -2 = 0.447213596 Reorder the terms: -2 + x = 0.447213596 Solving -2 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.447213596 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.447213596 + 2 x = 0.447213596 + 2 Combine like terms: 0.447213596 + 2 = 2.447213596 x = 2.447213596 Simplifying x = 2.447213596Subproblem 2
x + -2 = -0.447213596 Simplifying x + -2 = -0.447213596 Reorder the terms: -2 + x = -0.447213596 Solving -2 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.447213596 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.447213596 + 2 x = -0.447213596 + 2 Combine like terms: -0.447213596 + 2 = 1.552786404 x = 1.552786404 Simplifying x = 1.552786404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.447213596, 1.552786404}
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