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Simplifying x2 + -4x + -144 = 0 Reorder the terms: -144 + -4x + x2 = 0 Solving -144 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -4x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -4x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -4x + x2 = 0 + 144 -4x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -4x + x2 = 144 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 144 + 4 Reorder the terms: 4 + -4x + x2 = 144 + 4 Combine like terms: 144 + 4 = 148 4 + -4x + x2 = 148 Factor a perfect square on the left side: (x + -2)(x + -2) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + -2) equal to 12.165525061 and -12.165525061.Subproblem 1
x + -2 = 12.165525061 Simplifying x + -2 = 12.165525061 Reorder the terms: -2 + x = 12.165525061 Solving -2 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.165525061 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.165525061 + 2 x = 12.165525061 + 2 Combine like terms: 12.165525061 + 2 = 14.165525061 x = 14.165525061 Simplifying x = 14.165525061Subproblem 2
x + -2 = -12.165525061 Simplifying x + -2 = -12.165525061 Reorder the terms: -2 + x = -12.165525061 Solving -2 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.165525061 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.165525061 + 2 x = -12.165525061 + 2 Combine like terms: -12.165525061 + 2 = -10.165525061 x = -10.165525061 Simplifying x = -10.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.165525061, -10.165525061}
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