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Simplifying (4x + -32)(3x + 9) = 180 Reorder the terms: (-32 + 4x)(3x + 9) = 180 Reorder the terms: (-32 + 4x)(9 + 3x) = 180 Multiply (-32 + 4x) * (9 + 3x) (-32(9 + 3x) + 4x * (9 + 3x)) = 180 ((9 * -32 + 3x * -32) + 4x * (9 + 3x)) = 180 ((-288 + -96x) + 4x * (9 + 3x)) = 180 (-288 + -96x + (9 * 4x + 3x * 4x)) = 180 (-288 + -96x + (36x + 12x2)) = 180 Combine like terms: -96x + 36x = -60x (-288 + -60x + 12x2) = 180 Solving -288 + -60x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: -288 + -180 + -60x + 12x2 = 180 + -180 Combine like terms: -288 + -180 = -468 -468 + -60x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -468 + -60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-39 + -5x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-39 + -5x + x2)' equal to zero and attempt to solve: Simplifying -39 + -5x + x2 = 0 Solving -39 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -5x + x2 = 0 + 39 -5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -5x + x2 = 39 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 39 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 39 + 6.25 Combine like terms: 39 + 6.25 = 45.25 6.25 + -5x + x2 = 45.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -2.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -2.5 = 6.726812024 Simplifying x + -2.5 = 6.726812024 Reorder the terms: -2.5 + x = 6.726812024 Solving -2.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.726812024 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.726812024 + 2.5 x = 6.726812024 + 2.5 Combine like terms: 6.726812024 + 2.5 = 9.226812024 x = 9.226812024 Simplifying x = 9.226812024Subproblem 2
x + -2.5 = -6.726812024 Simplifying x + -2.5 = -6.726812024 Reorder the terms: -2.5 + x = -6.726812024 Solving -2.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.726812024 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.726812024 + 2.5 x = -6.726812024 + 2.5 Combine like terms: -6.726812024 + 2.5 = -4.226812024 x = -4.226812024 Simplifying x = -4.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.226812024, -4.226812024}Solution
x = {9.226812024, -4.226812024}
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