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Simplifying x2 + -2x + 9 = 35 Reorder the terms: 9 + -2x + x2 = 35 Solving 9 + -2x + x2 = 35 Solving for variable 'x'. Reorder the terms: 9 + -35 + -2x + x2 = 35 + -35 Combine like terms: 9 + -35 = -26 -26 + -2x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -26 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -2x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -2x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -2x + x2 = 0 + 26 -2x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -2x + x2 = 26 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 26 + 1 Reorder the terms: 1 + -2x + x2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + -2x + x2 = 27 Factor a perfect square on the left side: (x + -1)(x + -1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -1) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -1 = 5.196152423 Simplifying x + -1 = 5.196152423 Reorder the terms: -1 + x = 5.196152423 Solving -1 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.196152423 + 1 x = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 x = 6.196152423 Simplifying x = 6.196152423Subproblem 2
x + -1 = -5.196152423 Simplifying x + -1 = -5.196152423 Reorder the terms: -1 + x = -5.196152423 Solving -1 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.196152423 + 1 x = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 x = -4.196152423 Simplifying x = -4.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.196152423, -4.196152423}
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