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Simplifying 16x2 + 512x + -11264 = 0 Reorder the terms: -11264 + 512x + 16x2 = 0 Solving -11264 + 512x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-704 + 32x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-704 + 32x + x2)' equal to zero and attempt to solve: Simplifying -704 + 32x + x2 = 0 Solving -704 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '704' to each side of the equation. -704 + 32x + 704 + x2 = 0 + 704 Reorder the terms: -704 + 704 + 32x + x2 = 0 + 704 Combine like terms: -704 + 704 = 0 0 + 32x + x2 = 0 + 704 32x + x2 = 0 + 704 Combine like terms: 0 + 704 = 704 32x + x2 = 704 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 704 + 256 Reorder the terms: 256 + 32x + x2 = 704 + 256 Combine like terms: 704 + 256 = 960 256 + 32x + x2 = 960 Factor a perfect square on the left side: (x + 16)(x + 16) = 960 Calculate the square root of the right side: 30.98386677 Break this problem into two subproblems by setting (x + 16) equal to 30.98386677 and -30.98386677.Subproblem 1
x + 16 = 30.98386677 Simplifying x + 16 = 30.98386677 Reorder the terms: 16 + x = 30.98386677 Solving 16 + x = 30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 30.98386677 + -16 Combine like terms: 16 + -16 = 0 0 + x = 30.98386677 + -16 x = 30.98386677 + -16 Combine like terms: 30.98386677 + -16 = 14.98386677 x = 14.98386677 Simplifying x = 14.98386677Subproblem 2
x + 16 = -30.98386677 Simplifying x + 16 = -30.98386677 Reorder the terms: 16 + x = -30.98386677 Solving 16 + x = -30.98386677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -30.98386677 + -16 Combine like terms: 16 + -16 = 0 0 + x = -30.98386677 + -16 x = -30.98386677 + -16 Combine like terms: -30.98386677 + -16 = -46.98386677 x = -46.98386677 Simplifying x = -46.98386677Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.98386677, -46.98386677}Solution
x = {14.98386677, -46.98386677}
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