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Simplifying (4x + -1)(x + 8) = 1 Reorder the terms: (-1 + 4x)(x + 8) = 1 Reorder the terms: (-1 + 4x)(8 + x) = 1 Multiply (-1 + 4x) * (8 + x) (-1(8 + x) + 4x * (8 + x)) = 1 ((8 * -1 + x * -1) + 4x * (8 + x)) = 1 ((-8 + -1x) + 4x * (8 + x)) = 1 (-8 + -1x + (8 * 4x + x * 4x)) = 1 (-8 + -1x + (32x + 4x2)) = 1 Combine like terms: -1x + 32x = 31x (-8 + 31x + 4x2) = 1 Solving -8 + 31x + 4x2 = 1 Solving for variable 'x'. Reorder the terms: -8 + -1 + 31x + 4x2 = 1 + -1 Combine like terms: -8 + -1 = -9 -9 + 31x + 4x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -9 + 31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 7.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 7.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 7.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 7.75x + x2 = 0 + 2.25 7.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 7.75x + x2 = 2.25 The x term is 7.75x. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75x + 15.015625 + x2 = 2.25 + 15.015625 Reorder the terms: 15.015625 + 7.75x + x2 = 2.25 + 15.015625 Combine like terms: 2.25 + 15.015625 = 17.265625 15.015625 + 7.75x + x2 = 17.265625 Factor a perfect square on the left side: (x + 3.875)(x + 3.875) = 17.265625 Calculate the square root of the right side: 4.155192535 Break this problem into two subproblems by setting (x + 3.875) equal to 4.155192535 and -4.155192535.Subproblem 1
x + 3.875 = 4.155192535 Simplifying x + 3.875 = 4.155192535 Reorder the terms: 3.875 + x = 4.155192535 Solving 3.875 + x = 4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = 4.155192535 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = 4.155192535 + -3.875 x = 4.155192535 + -3.875 Combine like terms: 4.155192535 + -3.875 = 0.280192535 x = 0.280192535 Simplifying x = 0.280192535Subproblem 2
x + 3.875 = -4.155192535 Simplifying x + 3.875 = -4.155192535 Reorder the terms: 3.875 + x = -4.155192535 Solving 3.875 + x = -4.155192535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = -4.155192535 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = -4.155192535 + -3.875 x = -4.155192535 + -3.875 Combine like terms: -4.155192535 + -3.875 = -8.030192535 x = -8.030192535 Simplifying x = -8.030192535Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.280192535, -8.030192535}
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