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Simplifying x(x + -8)(4) = 448 Reorder the terms: x(-8 + x)(4) = 448 Reorder the terms for easier multiplication: 4x(-8 + x) = 448 (-8 * 4x + x * 4x) = 448 (-32x + 4x2) = 448 Solving -32x + 4x2 = 448 Solving for variable 'x'. Reorder the terms: -448 + -32x + 4x2 = 448 + -448 Combine like terms: 448 + -448 = 0 -448 + -32x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-112 + -8x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-112 + -8x + x2)' equal to zero and attempt to solve: Simplifying -112 + -8x + x2 = 0 Solving -112 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + -8x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + -8x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + -8x + x2 = 0 + 112 -8x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 -8x + x2 = 112 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 112 + 16 Reorder the terms: 16 + -8x + x2 = 112 + 16 Combine like terms: 112 + 16 = 128 16 + -8x + x2 = 128 Factor a perfect square on the left side: (x + -4)(x + -4) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -4) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -4 = 11.313708499 Simplifying x + -4 = 11.313708499 Reorder the terms: -4 + x = 11.313708499 Solving -4 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 11.313708499 + 4 Combine like terms: -4 + 4 = 0 0 + x = 11.313708499 + 4 x = 11.313708499 + 4 Combine like terms: 11.313708499 + 4 = 15.313708499 x = 15.313708499 Simplifying x = 15.313708499Subproblem 2
x + -4 = -11.313708499 Simplifying x + -4 = -11.313708499 Reorder the terms: -4 + x = -11.313708499 Solving -4 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -11.313708499 + 4 Combine like terms: -4 + 4 = 0 0 + x = -11.313708499 + 4 x = -11.313708499 + 4 Combine like terms: -11.313708499 + 4 = -7.313708499 x = -7.313708499 Simplifying x = -7.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.313708499, -7.313708499}Solution
x = {15.313708499, -7.313708499}
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