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Simplifying 35 = (2x + 2)(x + 4) Reorder the terms: 35 = (2 + 2x)(x + 4) Reorder the terms: 35 = (2 + 2x)(4 + x) Multiply (2 + 2x) * (4 + x) 35 = (2(4 + x) + 2x * (4 + x)) 35 = ((4 * 2 + x * 2) + 2x * (4 + x)) 35 = ((8 + 2x) + 2x * (4 + x)) 35 = (8 + 2x + (4 * 2x + x * 2x)) 35 = (8 + 2x + (8x + 2x2)) Combine like terms: 2x + 8x = 10x 35 = (8 + 10x + 2x2) Solving 35 = 8 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 35 + -8 = 27 27 + -10x + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2 Reorder the terms: 27 + -10x + -2x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 27 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 27 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 27 + -10x + -2x2 = 0 + 2x2 + -2x2 27 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 27 + -10x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13.5 + 5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 5x + x2 = 0 + 13.5 5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 5x + x2 = 13.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 13.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 13.5 + 6.25 Combine like terms: 13.5 + 6.25 = 19.75 6.25 + 5x + x2 = 19.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + 2.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + 2.5 = 4.444097209 Simplifying x + 2.5 = 4.444097209 Reorder the terms: 2.5 + x = 4.444097209 Solving 2.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.444097209 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.444097209 + -2.5 x = 4.444097209 + -2.5 Combine like terms: 4.444097209 + -2.5 = 1.944097209 x = 1.944097209 Simplifying x = 1.944097209Subproblem 2
x + 2.5 = -4.444097209 Simplifying x + 2.5 = -4.444097209 Reorder the terms: 2.5 + x = -4.444097209 Solving 2.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.444097209 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.444097209 + -2.5 x = -4.444097209 + -2.5 Combine like terms: -4.444097209 + -2.5 = -6.944097209 x = -6.944097209 Simplifying x = -6.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.944097209, -6.944097209}
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