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Simplifying x2 + -2x + -2 = 144 Reorder the terms: -2 + -2x + x2 = 144 Solving -2 + -2x + x2 = 144 Solving for variable 'x'. Reorder the terms: -2 + -144 + -2x + x2 = 144 + -144 Combine like terms: -2 + -144 = -146 -146 + -2x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -146 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + -2x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + -2x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + -2x + x2 = 0 + 146 -2x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 -2x + x2 = 146 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 = 146 + 1 Reorder the terms: 1 + -2x + x2 = 146 + 1 Combine like terms: 146 + 1 = 147 1 + -2x + x2 = 147 Factor a perfect square on the left side: (x + -1)(x + -1) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + -1) equal to 12.124355653 and -12.124355653.Subproblem 1
x + -1 = 12.124355653 Simplifying x + -1 = 12.124355653 Reorder the terms: -1 + x = 12.124355653 Solving -1 + x = 12.124355653 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 = 12.124355653 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.124355653 + 1 x = 12.124355653 + 1 Combine like terms: 12.124355653 + 1 = 13.124355653 x = 13.124355653 Simplifying x = 13.124355653Subproblem 2
x + -1 = -12.124355653 Simplifying x + -1 = -12.124355653 Reorder the terms: -1 + x = -12.124355653 Solving -1 + x = -12.124355653 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 = -12.124355653 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.124355653 + 1 x = -12.124355653 + 1 Combine like terms: -12.124355653 + 1 = -11.124355653 x = -11.124355653 Simplifying x = -11.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.124355653, -11.124355653}
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