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Simplifying (4x + 5)(4x + -5) = (4x + -5) * 2 + 10 Reorder the terms: (5 + 4x)(4x + -5) = (4x + -5) * 2 + 10 Reorder the terms: (5 + 4x)(-5 + 4x) = (4x + -5) * 2 + 10 Multiply (5 + 4x) * (-5 + 4x) (5(-5 + 4x) + 4x * (-5 + 4x)) = (4x + -5) * 2 + 10 ((-5 * 5 + 4x * 5) + 4x * (-5 + 4x)) = (4x + -5) * 2 + 10 ((-25 + 20x) + 4x * (-5 + 4x)) = (4x + -5) * 2 + 10 (-25 + 20x + (-5 * 4x + 4x * 4x)) = (4x + -5) * 2 + 10 (-25 + 20x + (-20x + 16x2)) = (4x + -5) * 2 + 10 Combine like terms: 20x + -20x = 0 (-25 + 0 + 16x2) = (4x + -5) * 2 + 10 (-25 + 16x2) = (4x + -5) * 2 + 10 Reorder the terms: -25 + 16x2 = (-5 + 4x) * 2 + 10 Reorder the terms for easier multiplication: -25 + 16x2 = 2(-5 + 4x) + 10 -25 + 16x2 = (-5 * 2 + 4x * 2) + 10 -25 + 16x2 = (-10 + 8x) + 10 Reorder the terms: -25 + 16x2 = -10 + 10 + 8x Combine like terms: -10 + 10 = 0 -25 + 16x2 = 0 + 8x -25 + 16x2 = 8x Solving -25 + 16x2 = 8x Solving for variable 'x'. Reorder the terms: -25 + -8x + 16x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -25 + -8x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -0.5x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -0.5x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -0.5x + x2 = 0 + 1.5625 -0.5x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -0.5x + x2 = 1.5625 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.5625 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.5625 + 0.0625 Combine like terms: 1.5625 + 0.0625 = 1.625 0.0625 + -0.5x + x2 = 1.625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + -0.25) equal to 1.274754878 and -1.274754878.Subproblem 1
x + -0.25 = 1.274754878 Simplifying x + -0.25 = 1.274754878 Reorder the terms: -0.25 + x = 1.274754878 Solving -0.25 + x = 1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.274754878 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.274754878 + 0.25 x = 1.274754878 + 0.25 Combine like terms: 1.274754878 + 0.25 = 1.524754878 x = 1.524754878 Simplifying x = 1.524754878Subproblem 2
x + -0.25 = -1.274754878 Simplifying x + -0.25 = -1.274754878 Reorder the terms: -0.25 + x = -1.274754878 Solving -0.25 + x = -1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.274754878 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.274754878 + 0.25 x = -1.274754878 + 0.25 Combine like terms: -1.274754878 + 0.25 = -1.024754878 x = -1.024754878 Simplifying x = -1.024754878Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.524754878, -1.024754878}
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