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Simplifying x2 + -8x + 16 + -2 = 25 Reorder the terms: 16 + -2 + -8x + x2 = 25 Combine like terms: 16 + -2 = 14 14 + -8x + x2 = 25 Solving 14 + -8x + x2 = 25 Solving for variable 'x'. Reorder the terms: 14 + -25 + -8x + x2 = 25 + -25 Combine like terms: 14 + -25 = -11 -11 + -8x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -11 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -8x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -8x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -8x + x2 = 0 + 11 -8x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -8x + x2 = 11 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 = 11 + 16 Reorder the terms: 16 + -8x + x2 = 11 + 16 Combine like terms: 11 + 16 = 27 16 + -8x + x2 = 27 Factor a perfect square on the left side: (x + -4)(x + -4) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -4) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -4 = 5.196152423 Simplifying x + -4 = 5.196152423 Reorder the terms: -4 + x = 5.196152423 Solving -4 + x = 5.196152423 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 = 5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.196152423 + 4 x = 5.196152423 + 4 Combine like terms: 5.196152423 + 4 = 9.196152423 x = 9.196152423 Simplifying x = 9.196152423Subproblem 2
x + -4 = -5.196152423 Simplifying x + -4 = -5.196152423 Reorder the terms: -4 + x = -5.196152423 Solving -4 + x = -5.196152423 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 = -5.196152423 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.196152423 + 4 x = -5.196152423 + 4 Combine like terms: -5.196152423 + 4 = -1.196152423 x = -1.196152423 Simplifying x = -1.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.196152423, -1.196152423}
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