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Simplifying x2 + 2x + 1 = 65 Reorder the terms: 1 + 2x + x2 = 65 Solving 1 + 2x + x2 = 65 Solving for variable 'x'. Reorder the terms: 1 + -65 + 2x + x2 = 65 + -65 Combine like terms: 1 + -65 = -64 -64 + 2x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -64 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 2x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 2x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 2x + x2 = 0 + 64 2x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 2x + x2 = 64 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 = 64 + 1 Reorder the terms: 1 + 2x + x2 = 64 + 1 Combine like terms: 64 + 1 = 65 1 + 2x + x2 = 65 Factor a perfect square on the left side: (x + 1)(x + 1) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 1) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 1 = 8.062257748 Simplifying x + 1 = 8.062257748 Reorder the terms: 1 + x = 8.062257748 Solving 1 + x = 8.062257748 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 = 8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.062257748 + -1 x = 8.062257748 + -1 Combine like terms: 8.062257748 + -1 = 7.062257748 x = 7.062257748 Simplifying x = 7.062257748Subproblem 2
x + 1 = -8.062257748 Simplifying x + 1 = -8.062257748 Reorder the terms: 1 + x = -8.062257748 Solving 1 + x = -8.062257748 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 = -8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.062257748 + -1 x = -8.062257748 + -1 Combine like terms: -8.062257748 + -1 = -9.062257748 x = -9.062257748 Simplifying x = -9.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.062257748, -9.062257748}
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