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Simplifying 4x2 + -25x + 19 = 0 Reorder the terms: 19 + -25x + 4x2 = 0 Solving 19 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -6.25x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -6.25x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -6.25x + x2 = 0 + -4.75 -6.25x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -6.25x + x2 = -4.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -4.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -4.75 + 9.765625 Combine like terms: -4.75 + 9.765625 = 5.015625 9.765625 + -6.25x + x2 = 5.015625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (x + -3.125) equal to 2.239559108 and -2.239559108.Subproblem 1
x + -3.125 = 2.239559108 Simplifying x + -3.125 = 2.239559108 Reorder the terms: -3.125 + x = 2.239559108 Solving -3.125 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.239559108 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.239559108 + 3.125 x = 2.239559108 + 3.125 Combine like terms: 2.239559108 + 3.125 = 5.364559108 x = 5.364559108 Simplifying x = 5.364559108Subproblem 2
x + -3.125 = -2.239559108 Simplifying x + -3.125 = -2.239559108 Reorder the terms: -3.125 + x = -2.239559108 Solving -3.125 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.239559108 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.239559108 + 3.125 x = -2.239559108 + 3.125 Combine like terms: -2.239559108 + 3.125 = 0.885440892 x = 0.885440892 Simplifying x = 0.885440892Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.364559108, 0.885440892}
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