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Simplifying 0 = -16x2 + 160x + 32 Reorder the terms: 0 = 32 + 160x + -16x2 Solving 0 = 32 + 160x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -160x + 16x2 = 32 + 160x + -16x2 + -32 + -160x + 16x2 Reorder the terms: -32 + -160x + 16x2 = 32 + -32 + 160x + -160x + -16x2 + 16x2 Combine like terms: 32 + -32 = 0 -32 + -160x + 16x2 = 0 + 160x + -160x + -16x2 + 16x2 -32 + -160x + 16x2 = 160x + -160x + -16x2 + 16x2 Combine like terms: 160x + -160x = 0 -32 + -160x + 16x2 = 0 + -16x2 + 16x2 -32 + -160x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -32 + -160x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-2 + -10x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-2 + -10x + x2)' equal to zero and attempt to solve: Simplifying -2 + -10x + x2 = 0 Solving -2 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -10x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -10x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -10x + x2 = 0 + 2 -10x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -10x + x2 = 2 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 2 + 25 Reorder the terms: 25 + -10x + x2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + -10x + x2 = 27 Factor a perfect square on the left side: (x + -5)(x + -5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -5) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -5 = 5.196152423 Simplifying x + -5 = 5.196152423 Reorder the terms: -5 + x = 5.196152423 Solving -5 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.196152423 + 5 x = 5.196152423 + 5 Combine like terms: 5.196152423 + 5 = 10.196152423 x = 10.196152423 Simplifying x = 10.196152423Subproblem 2
x + -5 = -5.196152423 Simplifying x + -5 = -5.196152423 Reorder the terms: -5 + x = -5.196152423 Solving -5 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.196152423 + 5 x = -5.196152423 + 5 Combine like terms: -5.196152423 + 5 = -0.196152423 x = -0.196152423 Simplifying x = -0.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.196152423, -0.196152423}Solution
x = {10.196152423, -0.196152423}
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