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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 = 4.196152423 x = 4.196152423 Simplifying x = 4.196152423Subproblem 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 = -6.196152423 x = -6.196152423 Simplifying x = -6.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.196152423, -6.196152423}
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