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Simplifying x2 + 2x + -67 = 0 Reorder the terms: -67 + 2x + x2 = 0 Solving -67 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 2x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + 2x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 2x + x2 = 0 + 67 2x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 2x + x2 = 67 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 = 67 + 1 Reorder the terms: 1 + 2x + x2 = 67 + 1 Combine like terms: 67 + 1 = 68 1 + 2x + x2 = 68 Factor a perfect square on the left side: (x + 1)(x + 1) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + 1) equal to 8.246211251 and -8.246211251.Subproblem 1
x + 1 = 8.246211251 Simplifying x + 1 = 8.246211251 Reorder the terms: 1 + x = 8.246211251 Solving 1 + x = 8.246211251 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 = 8.246211251 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.246211251 + -1 x = 8.246211251 + -1 Combine like terms: 8.246211251 + -1 = 7.246211251 x = 7.246211251 Simplifying x = 7.246211251Subproblem 2
x + 1 = -8.246211251 Simplifying x + 1 = -8.246211251 Reorder the terms: 1 + x = -8.246211251 Solving 1 + x = -8.246211251 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 = -8.246211251 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.246211251 + -1 x = -8.246211251 + -1 Combine like terms: -8.246211251 + -1 = -9.246211251 x = -9.246211251 Simplifying x = -9.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.246211251, -9.246211251}
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