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Simplifying x2 + 4x + 11 = 80 Reorder the terms: 11 + 4x + x2 = 80 Solving 11 + 4x + x2 = 80 Solving for variable 'x'. Reorder the terms: 11 + -80 + 4x + x2 = 80 + -80 Combine like terms: 11 + -80 = -69 -69 + 4x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -69 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 4x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + 4x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 4x + x2 = 0 + 69 4x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 4x + x2 = 69 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 = 69 + 4 Reorder the terms: 4 + 4x + x2 = 69 + 4 Combine like terms: 69 + 4 = 73 4 + 4x + x2 = 73 Factor a perfect square on the left side: (x + 2)(x + 2) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 2) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 2 = 8.544003745 Simplifying x + 2 = 8.544003745 Reorder the terms: 2 + x = 8.544003745 Solving 2 + x = 8.544003745 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 = 8.544003745 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.544003745 + -2 x = 8.544003745 + -2 Combine like terms: 8.544003745 + -2 = 6.544003745 x = 6.544003745 Simplifying x = 6.544003745Subproblem 2
x + 2 = -8.544003745 Simplifying x + 2 = -8.544003745 Reorder the terms: 2 + x = -8.544003745 Solving 2 + x = -8.544003745 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 = -8.544003745 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.544003745 + -2 x = -8.544003745 + -2 Combine like terms: -8.544003745 + -2 = -10.544003745 x = -10.544003745 Simplifying x = -10.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.544003745, -10.544003745}
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