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Simplifying 3(4x + -3)(4x + 3) = 48x Reorder the terms: 3(-3 + 4x)(4x + 3) = 48x Reorder the terms: 3(-3 + 4x)(3 + 4x) = 48x Multiply (-3 + 4x) * (3 + 4x) 3(-3(3 + 4x) + 4x * (3 + 4x)) = 48x 3((3 * -3 + 4x * -3) + 4x * (3 + 4x)) = 48x 3((-9 + -12x) + 4x * (3 + 4x)) = 48x 3(-9 + -12x + (3 * 4x + 4x * 4x)) = 48x 3(-9 + -12x + (12x + 16x2)) = 48x Combine like terms: -12x + 12x = 0 3(-9 + 0 + 16x2) = 48x 3(-9 + 16x2) = 48x (-9 * 3 + 16x2 * 3) = 48x (-27 + 48x2) = 48x Solving -27 + 48x2 = 48x Solving for variable 'x'. Reorder the terms: -27 + -48x + 48x2 = 48x + -48x Combine like terms: 48x + -48x = 0 -27 + -48x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -16x + 16x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -16x + 16x2)' equal to zero and attempt to solve: Simplifying -9 + -16x + 16x2 = 0 Solving -9 + -16x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + -1x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -1x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -1x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -1x + x2 = 0 + 0.5625 -1x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -1x + x2 = 0.5625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.5625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.5625 + 0.25 Combine like terms: 0.5625 + 0.25 = 0.8125 0.25 + -1x + x2 = 0.8125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + -0.5) equal to 0.901387819 and -0.901387819.Subproblem 1
x + -0.5 = 0.901387819 Simplifying x + -0.5 = 0.901387819 Reorder the terms: -0.5 + x = 0.901387819 Solving -0.5 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.901387819 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.901387819 + 0.5 x = 0.901387819 + 0.5 Combine like terms: 0.901387819 + 0.5 = 1.401387819 x = 1.401387819 Simplifying x = 1.401387819Subproblem 2
x + -0.5 = -0.901387819 Simplifying x + -0.5 = -0.901387819 Reorder the terms: -0.5 + x = -0.901387819 Solving -0.5 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.901387819 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.901387819 + 0.5 x = -0.901387819 + 0.5 Combine like terms: -0.901387819 + 0.5 = -0.401387819 x = -0.401387819 Simplifying x = -0.401387819Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.401387819, -0.401387819}Solution
x = {1.401387819, -0.401387819}
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