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Simplifying (4x + 1)(x + -8) = 8 Reorder the terms: (1 + 4x)(x + -8) = 8 Reorder the terms: (1 + 4x)(-8 + x) = 8 Multiply (1 + 4x) * (-8 + x) (1(-8 + x) + 4x * (-8 + x)) = 8 ((-8 * 1 + x * 1) + 4x * (-8 + x)) = 8 ((-8 + 1x) + 4x * (-8 + x)) = 8 (-8 + 1x + (-8 * 4x + x * 4x)) = 8 (-8 + 1x + (-32x + 4x2)) = 8 Combine like terms: 1x + -32x = -31x (-8 + -31x + 4x2) = 8 Solving -8 + -31x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -8 + -31x + 4x2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + -31x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -7.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -7.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -7.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7.75x + x2 = 0 + 4 -7.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -7.75x + x2 = 4 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 = 4 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 4 + 15.015625 Combine like terms: 4 + 15.015625 = 19.015625 15.015625 + -7.75x + x2 = 19.015625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 19.015625 Calculate the square root of the right side: 4.360690886 Break this problem into two subproblems by setting (x + -3.875) equal to 4.360690886 and -4.360690886.Subproblem 1
x + -3.875 = 4.360690886 Simplifying x + -3.875 = 4.360690886 Reorder the terms: -3.875 + x = 4.360690886 Solving -3.875 + x = 4.360690886 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 = 4.360690886 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 4.360690886 + 3.875 x = 4.360690886 + 3.875 Combine like terms: 4.360690886 + 3.875 = 8.235690886 x = 8.235690886 Simplifying x = 8.235690886Subproblem 2
x + -3.875 = -4.360690886 Simplifying x + -3.875 = -4.360690886 Reorder the terms: -3.875 + x = -4.360690886 Solving -3.875 + x = -4.360690886 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 = -4.360690886 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -4.360690886 + 3.875 x = -4.360690886 + 3.875 Combine like terms: -4.360690886 + 3.875 = -0.485690886 x = -0.485690886 Simplifying x = -0.485690886Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.235690886, -0.485690886}
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