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Simplifying x2 + -2x + -2 = 65 Reorder the terms: -2 + -2x + x2 = 65 Solving -2 + -2x + x2 = 65 Solving for variable 'x'. Reorder the terms: -2 + -65 + -2x + x2 = 65 + -65 Combine like terms: -2 + -65 = -67 -67 + -2x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -67 + -2x + x2 = 0 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 = 9.246211251 x = 9.246211251 Simplifying x = 9.246211251Subproblem 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 = -7.246211251 x = -7.246211251 Simplifying x = -7.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.246211251, -7.246211251}
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