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Simplifying (2x + 1)(x + -8) = 8 Reorder the terms: (1 + 2x)(x + -8) = 8 Reorder the terms: (1 + 2x)(-8 + x) = 8 Multiply (1 + 2x) * (-8 + x) (1(-8 + x) + 2x * (-8 + x)) = 8 ((-8 * 1 + x * 1) + 2x * (-8 + x)) = 8 ((-8 + 1x) + 2x * (-8 + x)) = 8 (-8 + 1x + (-8 * 2x + x * 2x)) = 8 (-8 + 1x + (-16x + 2x2)) = 8 Combine like terms: 1x + -16x = -15x (-8 + -15x + 2x2) = 8 Solving -8 + -15x + 2x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -8 + -15x + 2x2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + -15x + 2x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -7.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -7.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7.5x + x2 = 0 + 8 -7.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7.5x + x2 = 8 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 8 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 8 + 14.0625 Combine like terms: 8 + 14.0625 = 22.0625 14.0625 + -7.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -3.75) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -3.75 = 4.697073557 Simplifying x + -3.75 = 4.697073557 Reorder the terms: -3.75 + x = 4.697073557 Solving -3.75 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.697073557 + 3.75 x = 4.697073557 + 3.75 Combine like terms: 4.697073557 + 3.75 = 8.447073557 x = 8.447073557 Simplifying x = 8.447073557Subproblem 2
x + -3.75 = -4.697073557 Simplifying x + -3.75 = -4.697073557 Reorder the terms: -3.75 + x = -4.697073557 Solving -3.75 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.697073557 + 3.75 x = -4.697073557 + 3.75 Combine like terms: -4.697073557 + 3.75 = -0.947073557 x = -0.947073557 Simplifying x = -0.947073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.447073557, -0.947073557}
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