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Simplifying x + (x + 2)(x + 4) = 33 Reorder the terms: x + (2 + x)(x + 4) = 33 Reorder the terms: x + (2 + x)(4 + x) = 33 Multiply (2 + x) * (4 + x) x + (2(4 + x) + x(4 + x)) = 33 x + ((4 * 2 + x * 2) + x(4 + x)) = 33 x + ((8 + 2x) + x(4 + x)) = 33 x + (8 + 2x + (4 * x + x * x)) = 33 x + (8 + 2x + (4x + x2)) = 33 Combine like terms: 2x + 4x = 6x x + (8 + 6x + x2) = 33 Reorder the terms: 8 + x + 6x + x2 = 33 Combine like terms: x + 6x = 7x 8 + 7x + x2 = 33 Solving 8 + 7x + x2 = 33 Solving for variable 'x'. Reorder the terms: 8 + -33 + 7x + x2 = 33 + -33 Combine like terms: 8 + -33 = -25 -25 + 7x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -25 + 7x + x2 = 0 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 = 2.603277808 x = 2.603277808 Simplifying x = 2.603277808Subproblem 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 = -9.603277808 x = -9.603277808 Simplifying x = -9.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.603277808, -9.603277808}
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