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Simplifying 5x + 19 = 4x2 + -20x + 10 Reorder the terms: 19 + 5x = 4x2 + -20x + 10 Reorder the terms: 19 + 5x = 10 + -20x + 4x2 Solving 19 + 5x = 10 + -20x + 4x2 Solving for variable 'x'. Reorder the terms: 19 + -10 + 5x + 20x + -4x2 = 10 + -20x + 4x2 + -10 + 20x + -4x2 Combine like terms: 19 + -10 = 9 9 + 5x + 20x + -4x2 = 10 + -20x + 4x2 + -10 + 20x + -4x2 Combine like terms: 5x + 20x = 25x 9 + 25x + -4x2 = 10 + -20x + 4x2 + -10 + 20x + -4x2 Reorder the terms: 9 + 25x + -4x2 = 10 + -10 + -20x + 20x + 4x2 + -4x2 Combine like terms: 10 + -10 = 0 9 + 25x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2 9 + 25x + -4x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 9 + 25x + -4x2 = 0 + 4x2 + -4x2 9 + 25x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -6.25x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -6.25x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -6.25x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -6.25x + x2 = 0 + 2.25 -6.25x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -6.25x + x2 = 2.25 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 = 2.25 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 2.25 + 9.765625 Combine like terms: 2.25 + 9.765625 = 12.015625 9.765625 + -6.25x + x2 = 12.015625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 12.015625 Calculate the square root of the right side: 3.466356156 Break this problem into two subproblems by setting (x + -3.125) equal to 3.466356156 and -3.466356156.Subproblem 1
x + -3.125 = 3.466356156 Simplifying x + -3.125 = 3.466356156 Reorder the terms: -3.125 + x = 3.466356156 Solving -3.125 + x = 3.466356156 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 = 3.466356156 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.466356156 + 3.125 x = 3.466356156 + 3.125 Combine like terms: 3.466356156 + 3.125 = 6.591356156 x = 6.591356156 Simplifying x = 6.591356156Subproblem 2
x + -3.125 = -3.466356156 Simplifying x + -3.125 = -3.466356156 Reorder the terms: -3.125 + x = -3.466356156 Solving -3.125 + x = -3.466356156 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 = -3.466356156 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.466356156 + 3.125 x = -3.466356156 + 3.125 Combine like terms: -3.466356156 + 3.125 = -0.341356156 x = -0.341356156 Simplifying x = -0.341356156Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.591356156, -0.341356156}
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