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Simplifying x2 + 4x + 4 + -11x + -22 + -7 = 0 Reorder the terms: 4 + -22 + -7 + 4x + -11x + x2 = 0 Combine like terms: 4 + -22 = -18 -18 + -7 + 4x + -11x + x2 = 0 Combine like terms: -18 + -7 = -25 -25 + 4x + -11x + x2 = 0 Combine like terms: 4x + -11x = -7x -25 + -7x + x2 = 0 Solving -25 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -7x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -7x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -7x + x2 = 0 + 25 -7x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -7x + x2 = 25 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 25 + 12.25 Combine like terms: 25 + 12.25 = 37.25 12.25 + -7x + x2 = 37.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + -3.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + -3.5 = 6.103277808 Simplifying x + -3.5 = 6.103277808 Reorder the terms: -3.5 + x = 6.103277808 Solving -3.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 6.103277808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.103277808 + 3.5 x = 6.103277808 + 3.5 Combine like terms: 6.103277808 + 3.5 = 9.603277808 x = 9.603277808 Simplifying x = 9.603277808Subproblem 2
x + -3.5 = -6.103277808 Simplifying x + -3.5 = -6.103277808 Reorder the terms: -3.5 + x = -6.103277808 Solving -3.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -6.103277808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.103277808 + 3.5 x = -6.103277808 + 3.5 Combine like terms: -6.103277808 + 3.5 = -2.603277808 x = -2.603277808 Simplifying x = -2.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.603277808, -2.603277808}
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