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Simplifying x2 + 17x + -8 = 12x + 12 Reorder the terms: -8 + 17x + x2 = 12x + 12 Reorder the terms: -8 + 17x + x2 = 12 + 12x Solving -8 + 17x + x2 = 12 + 12x Solving for variable 'x'. Reorder the terms: -8 + -12 + 17x + -12x + x2 = 12 + 12x + -12 + -12x Combine like terms: -8 + -12 = -20 -20 + 17x + -12x + x2 = 12 + 12x + -12 + -12x Combine like terms: 17x + -12x = 5x -20 + 5x + x2 = 12 + 12x + -12 + -12x Reorder the terms: -20 + 5x + x2 = 12 + -12 + 12x + -12x Combine like terms: 12 + -12 = 0 -20 + 5x + x2 = 0 + 12x + -12x -20 + 5x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -20 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 5x + x2 = 0 + 20 5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 5x + x2 = 20 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 = 20 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 20 + 6.25 Combine like terms: 20 + 6.25 = 26.25 6.25 + 5x + x2 = 26.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 2.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 2.5 = 5.123475383 Simplifying x + 2.5 = 5.123475383 Reorder the terms: 2.5 + x = 5.123475383 Solving 2.5 + x = 5.123475383 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 = 5.123475383 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.123475383 + -2.5 x = 5.123475383 + -2.5 Combine like terms: 5.123475383 + -2.5 = 2.623475383 x = 2.623475383 Simplifying x = 2.623475383Subproblem 2
x + 2.5 = -5.123475383 Simplifying x + 2.5 = -5.123475383 Reorder the terms: 2.5 + x = -5.123475383 Solving 2.5 + x = -5.123475383 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 = -5.123475383 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.123475383 + -2.5 x = -5.123475383 + -2.5 Combine like terms: -5.123475383 + -2.5 = -7.623475383 x = -7.623475383 Simplifying x = -7.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.623475383, -7.623475383}
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