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Simplifying (2x + -2)(x + -2) = 448 Reorder the terms: (-2 + 2x)(x + -2) = 448 Reorder the terms: (-2 + 2x)(-2 + x) = 448 Multiply (-2 + 2x) * (-2 + x) (-2(-2 + x) + 2x * (-2 + x)) = 448 ((-2 * -2 + x * -2) + 2x * (-2 + x)) = 448 ((4 + -2x) + 2x * (-2 + x)) = 448 (4 + -2x + (-2 * 2x + x * 2x)) = 448 (4 + -2x + (-4x + 2x2)) = 448 Combine like terms: -2x + -4x = -6x (4 + -6x + 2x2) = 448 Solving 4 + -6x + 2x2 = 448 Solving for variable 'x'. Reorder the terms: 4 + -448 + -6x + 2x2 = 448 + -448 Combine like terms: 4 + -448 = -444 -444 + -6x + 2x2 = 448 + -448 Combine like terms: 448 + -448 = 0 -444 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-222 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-222 + -3x + x2)' equal to zero and attempt to solve: Simplifying -222 + -3x + x2 = 0 Solving -222 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '222' to each side of the equation. -222 + -3x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + -3x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + -3x + x2 = 0 + 222 -3x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 -3x + x2 = 222 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 222 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 222 + 2.25 Combine like terms: 222 + 2.25 = 224.25 2.25 + -3x + x2 = 224.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 224.25 Calculate the square root of the right side: 14.974979132 Break this problem into two subproblems by setting (x + -1.5) equal to 14.974979132 and -14.974979132.Subproblem 1
x + -1.5 = 14.974979132 Simplifying x + -1.5 = 14.974979132 Reorder the terms: -1.5 + x = 14.974979132 Solving -1.5 + x = 14.974979132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 14.974979132 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 14.974979132 + 1.5 x = 14.974979132 + 1.5 Combine like terms: 14.974979132 + 1.5 = 16.474979132 x = 16.474979132 Simplifying x = 16.474979132Subproblem 2
x + -1.5 = -14.974979132 Simplifying x + -1.5 = -14.974979132 Reorder the terms: -1.5 + x = -14.974979132 Solving -1.5 + x = -14.974979132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -14.974979132 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -14.974979132 + 1.5 x = -14.974979132 + 1.5 Combine like terms: -14.974979132 + 1.5 = -13.474979132 x = -13.474979132 Simplifying x = -13.474979132Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.474979132, -13.474979132}Solution
x = {16.474979132, -13.474979132}
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