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Simplifying (x + -7)(x + 2) = 17 Reorder the terms: (-7 + x)(x + 2) = 17 Reorder the terms: (-7 + x)(2 + x) = 17 Multiply (-7 + x) * (2 + x) (-7(2 + x) + x(2 + x)) = 17 ((2 * -7 + x * -7) + x(2 + x)) = 17 ((-14 + -7x) + x(2 + x)) = 17 (-14 + -7x + (2 * x + x * x)) = 17 (-14 + -7x + (2x + x2)) = 17 Combine like terms: -7x + 2x = -5x (-14 + -5x + x2) = 17 Solving -14 + -5x + x2 = 17 Solving for variable 'x'. Reorder the terms: -14 + -17 + -5x + x2 = 17 + -17 Combine like terms: -14 + -17 = -31 -31 + -5x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -31 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -5x + x2 = 0 + 31 -5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -5x + x2 = 31 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 = 31 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 31 + 6.25 Combine like terms: 31 + 6.25 = 37.25 6.25 + -5x + x2 = 37.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + -2.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + -2.5 = 6.103277808 Simplifying x + -2.5 = 6.103277808 Reorder the terms: -2.5 + x = 6.103277808 Solving -2.5 + x = 6.103277808 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 = 6.103277808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.103277808 + 2.5 x = 6.103277808 + 2.5 Combine like terms: 6.103277808 + 2.5 = 8.603277808 x = 8.603277808 Simplifying x = 8.603277808Subproblem 2
x + -2.5 = -6.103277808 Simplifying x + -2.5 = -6.103277808 Reorder the terms: -2.5 + x = -6.103277808 Solving -2.5 + x = -6.103277808 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 = -6.103277808 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.103277808 + 2.5 x = -6.103277808 + 2.5 Combine like terms: -6.103277808 + 2.5 = -3.603277808 x = -3.603277808 Simplifying x = -3.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.603277808, -3.603277808}
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