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Simplifying (4x + -5)(x + -5) = 16x + 20 Reorder the terms: (-5 + 4x)(x + -5) = 16x + 20 Reorder the terms: (-5 + 4x)(-5 + x) = 16x + 20 Multiply (-5 + 4x) * (-5 + x) (-5(-5 + x) + 4x * (-5 + x)) = 16x + 20 ((-5 * -5 + x * -5) + 4x * (-5 + x)) = 16x + 20 ((25 + -5x) + 4x * (-5 + x)) = 16x + 20 (25 + -5x + (-5 * 4x + x * 4x)) = 16x + 20 (25 + -5x + (-20x + 4x2)) = 16x + 20 Combine like terms: -5x + -20x = -25x (25 + -25x + 4x2) = 16x + 20 Reorder the terms: 25 + -25x + 4x2 = 20 + 16x Solving 25 + -25x + 4x2 = 20 + 16x Solving for variable 'x'. Reorder the terms: 25 + -20 + -25x + -16x + 4x2 = 20 + 16x + -20 + -16x Combine like terms: 25 + -20 = 5 5 + -25x + -16x + 4x2 = 20 + 16x + -20 + -16x Combine like terms: -25x + -16x = -41x 5 + -41x + 4x2 = 20 + 16x + -20 + -16x Reorder the terms: 5 + -41x + 4x2 = 20 + -20 + 16x + -16x Combine like terms: 20 + -20 = 0 5 + -41x + 4x2 = 0 + 16x + -16x 5 + -41x + 4x2 = 16x + -16x Combine like terms: 16x + -16x = 0 5 + -41x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -10.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -10.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -10.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -10.25x + x2 = 0 + -1.25 -10.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -10.25x + x2 = -1.25 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = -1.25 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -1.25 + 26.265625 Combine like terms: -1.25 + 26.265625 = 25.015625 26.265625 + -10.25x + x2 = 25.015625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 25.015625 Calculate the square root of the right side: 5.001562256 Break this problem into two subproblems by setting (x + -5.125) equal to 5.001562256 and -5.001562256.Subproblem 1
x + -5.125 = 5.001562256 Simplifying x + -5.125 = 5.001562256 Reorder the terms: -5.125 + x = 5.001562256 Solving -5.125 + x = 5.001562256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 5.001562256 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 5.001562256 + 5.125 x = 5.001562256 + 5.125 Combine like terms: 5.001562256 + 5.125 = 10.126562256 x = 10.126562256 Simplifying x = 10.126562256Subproblem 2
x + -5.125 = -5.001562256 Simplifying x + -5.125 = -5.001562256 Reorder the terms: -5.125 + x = -5.001562256 Solving -5.125 + x = -5.001562256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -5.001562256 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -5.001562256 + 5.125 x = -5.001562256 + 5.125 Combine like terms: -5.001562256 + 5.125 = 0.123437744 x = 0.123437744 Simplifying x = 0.123437744Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.126562256, 0.123437744}
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