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Simplifying x2 + -24x + -122 = 0 Reorder the terms: -122 + -24x + x2 = 0 Solving -122 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + -24x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + -24x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + -24x + x2 = 0 + 122 -24x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 -24x + x2 = 122 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 122 + 144 Reorder the terms: 144 + -24x + x2 = 122 + 144 Combine like terms: 122 + 144 = 266 144 + -24x + x2 = 266 Factor a perfect square on the left side: (x + -12)(x + -12) = 266 Calculate the square root of the right side: 16.30950643 Break this problem into two subproblems by setting (x + -12) equal to 16.30950643 and -16.30950643.Subproblem 1
x + -12 = 16.30950643 Simplifying x + -12 = 16.30950643 Reorder the terms: -12 + x = 16.30950643 Solving -12 + x = 16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 16.30950643 + 12 Combine like terms: -12 + 12 = 0 0 + x = 16.30950643 + 12 x = 16.30950643 + 12 Combine like terms: 16.30950643 + 12 = 28.30950643 x = 28.30950643 Simplifying x = 28.30950643Subproblem 2
x + -12 = -16.30950643 Simplifying x + -12 = -16.30950643 Reorder the terms: -12 + x = -16.30950643 Solving -12 + x = -16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -16.30950643 + 12 Combine like terms: -12 + 12 = 0 0 + x = -16.30950643 + 12 x = -16.30950643 + 12 Combine like terms: -16.30950643 + 12 = -4.30950643 x = -4.30950643 Simplifying x = -4.30950643Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.30950643, -4.30950643}
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