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Simplifying x2 + 4x + -110 = 0 Reorder the terms: -110 + 4x + x2 = 0 Solving -110 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 4x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 4x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 4x + x2 = 0 + 110 4x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 4x + x2 = 110 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 = 110 + 4 Reorder the terms: 4 + 4x + x2 = 110 + 4 Combine like terms: 110 + 4 = 114 4 + 4x + x2 = 114 Factor a perfect square on the left side: (x + 2)(x + 2) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + 2) equal to 10.677078252 and -10.677078252.Subproblem 1
x + 2 = 10.677078252 Simplifying x + 2 = 10.677078252 Reorder the terms: 2 + x = 10.677078252 Solving 2 + x = 10.677078252 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 = 10.677078252 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.677078252 + -2 x = 10.677078252 + -2 Combine like terms: 10.677078252 + -2 = 8.677078252 x = 8.677078252 Simplifying x = 8.677078252Subproblem 2
x + 2 = -10.677078252 Simplifying x + 2 = -10.677078252 Reorder the terms: 2 + x = -10.677078252 Solving 2 + x = -10.677078252 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 = -10.677078252 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.677078252 + -2 x = -10.677078252 + -2 Combine like terms: -10.677078252 + -2 = -12.677078252 x = -12.677078252 Simplifying x = -12.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.677078252, -12.677078252}
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