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Simplifying (3x + -17)(2x + 8) = 1 Reorder the terms: (-17 + 3x)(2x + 8) = 1 Reorder the terms: (-17 + 3x)(8 + 2x) = 1 Multiply (-17 + 3x) * (8 + 2x) (-17(8 + 2x) + 3x * (8 + 2x)) = 1 ((8 * -17 + 2x * -17) + 3x * (8 + 2x)) = 1 ((-136 + -34x) + 3x * (8 + 2x)) = 1 (-136 + -34x + (8 * 3x + 2x * 3x)) = 1 (-136 + -34x + (24x + 6x2)) = 1 Combine like terms: -34x + 24x = -10x (-136 + -10x + 6x2) = 1 Solving -136 + -10x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: -136 + -1 + -10x + 6x2 = 1 + -1 Combine like terms: -136 + -1 = -137 -137 + -10x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -137 + -10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -22.83333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '22.83333333' to each side of the equation. -22.83333333 + -1.666666667x + 22.83333333 + x2 = 0 + 22.83333333 Reorder the terms: -22.83333333 + 22.83333333 + -1.666666667x + x2 = 0 + 22.83333333 Combine like terms: -22.83333333 + 22.83333333 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 22.83333333 -1.666666667x + x2 = 0 + 22.83333333 Combine like terms: 0 + 22.83333333 = 22.83333333 -1.666666667x + x2 = 22.83333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 22.83333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 22.83333333 + 0.6944444447 Combine like terms: 22.83333333 + 0.6944444447 = 23.5277777747 0.6944444447 + -1.666666667x + x2 = 23.5277777747 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 23.5277777747 Calculate the square root of the right side: 4.85054407 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 4.85054407 and -4.85054407.Subproblem 1
x + -0.8333333335 = 4.85054407 Simplifying x + -0.8333333335 = 4.85054407 Reorder the terms: -0.8333333335 + x = 4.85054407 Solving -0.8333333335 + x = 4.85054407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 4.85054407 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 4.85054407 + 0.8333333335 x = 4.85054407 + 0.8333333335 Combine like terms: 4.85054407 + 0.8333333335 = 5.6838774035 x = 5.6838774035 Simplifying x = 5.6838774035Subproblem 2
x + -0.8333333335 = -4.85054407 Simplifying x + -0.8333333335 = -4.85054407 Reorder the terms: -0.8333333335 + x = -4.85054407 Solving -0.8333333335 + x = -4.85054407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -4.85054407 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -4.85054407 + 0.8333333335 x = -4.85054407 + 0.8333333335 Combine like terms: -4.85054407 + 0.8333333335 = -4.0172107365 x = -4.0172107365 Simplifying x = -4.0172107365Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.6838774035, -4.0172107365}
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