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Simplifying (2x + -5) * 2 + -1(x + 2)(3 + -4x) = 0 Reorder the terms: (-5 + 2x) * 2 + -1(x + 2)(3 + -4x) = 0 Reorder the terms for easier multiplication: 2(-5 + 2x) + -1(x + 2)(3 + -4x) = 0 (-5 * 2 + 2x * 2) + -1(x + 2)(3 + -4x) = 0 (-10 + 4x) + -1(x + 2)(3 + -4x) = 0 Reorder the terms: -10 + 4x + -1(2 + x)(3 + -4x) = 0 Multiply (2 + x) * (3 + -4x) -10 + 4x + -1(2(3 + -4x) + x(3 + -4x)) = 0 -10 + 4x + -1((3 * 2 + -4x * 2) + x(3 + -4x)) = 0 -10 + 4x + -1((6 + -8x) + x(3 + -4x)) = 0 -10 + 4x + -1(6 + -8x + (3 * x + -4x * x)) = 0 -10 + 4x + -1(6 + -8x + (3x + -4x2)) = 0 Combine like terms: -8x + 3x = -5x -10 + 4x + -1(6 + -5x + -4x2) = 0 -10 + 4x + (6 * -1 + -5x * -1 + -4x2 * -1) = 0 -10 + 4x + (-6 + 5x + 4x2) = 0 Reorder the terms: -10 + -6 + 4x + 5x + 4x2 = 0 Combine like terms: -10 + -6 = -16 -16 + 4x + 5x + 4x2 = 0 Combine like terms: 4x + 5x = 9x -16 + 9x + 4x2 = 0 Solving -16 + 9x + 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 + 2.25x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.25x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.25x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.25x + x2 = 0 + 4 2.25x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.25x + x2 = 4 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 4 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 4 + 1.265625 Combine like terms: 4 + 1.265625 = 5.265625 1.265625 + 2.25x + x2 = 5.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + 1.125) equal to 2.294694969 and -2.294694969.Subproblem 1
x + 1.125 = 2.294694969 Simplifying x + 1.125 = 2.294694969 Reorder the terms: 1.125 + x = 2.294694969 Solving 1.125 + x = 2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.294694969 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.294694969 + -1.125 x = 2.294694969 + -1.125 Combine like terms: 2.294694969 + -1.125 = 1.169694969 x = 1.169694969 Simplifying x = 1.169694969Subproblem 2
x + 1.125 = -2.294694969 Simplifying x + 1.125 = -2.294694969 Reorder the terms: 1.125 + x = -2.294694969 Solving 1.125 + x = -2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.294694969 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.294694969 + -1.125 x = -2.294694969 + -1.125 Combine like terms: -2.294694969 + -1.125 = -3.419694969 x = -3.419694969 Simplifying x = -3.419694969Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.169694969, -3.419694969}
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