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Simplifying (8x + -1)(x + 7) = 9 Reorder the terms: (-1 + 8x)(x + 7) = 9 Reorder the terms: (-1 + 8x)(7 + x) = 9 Multiply (-1 + 8x) * (7 + x) (-1(7 + x) + 8x * (7 + x)) = 9 ((7 * -1 + x * -1) + 8x * (7 + x)) = 9 ((-7 + -1x) + 8x * (7 + x)) = 9 (-7 + -1x + (7 * 8x + x * 8x)) = 9 (-7 + -1x + (56x + 8x2)) = 9 Combine like terms: -1x + 56x = 55x (-7 + 55x + 8x2) = 9 Solving -7 + 55x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -7 + -9 + 55x + 8x2 = 9 + -9 Combine like terms: -7 + -9 = -16 -16 + 55x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -16 + 55x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + 6.875x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6.875x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6.875x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6.875x + x2 = 0 + 2 6.875x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6.875x + x2 = 2 The x term is 6.875x. Take half its coefficient (3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. 6.875x + 11.81640625 + x2 = 2 + 11.81640625 Reorder the terms: 11.81640625 + 6.875x + x2 = 2 + 11.81640625 Combine like terms: 2 + 11.81640625 = 13.81640625 11.81640625 + 6.875x + x2 = 13.81640625 Factor a perfect square on the left side: (x + 3.4375)(x + 3.4375) = 13.81640625 Calculate the square root of the right side: 3.717042675 Break this problem into two subproblems by setting (x + 3.4375) equal to 3.717042675 and -3.717042675.Subproblem 1
x + 3.4375 = 3.717042675 Simplifying x + 3.4375 = 3.717042675 Reorder the terms: 3.4375 + x = 3.717042675 Solving 3.4375 + x = 3.717042675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = 3.717042675 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = 3.717042675 + -3.4375 x = 3.717042675 + -3.4375 Combine like terms: 3.717042675 + -3.4375 = 0.279542675 x = 0.279542675 Simplifying x = 0.279542675Subproblem 2
x + 3.4375 = -3.717042675 Simplifying x + 3.4375 = -3.717042675 Reorder the terms: 3.4375 + x = -3.717042675 Solving 3.4375 + x = -3.717042675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + x = -3.717042675 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + x = -3.717042675 + -3.4375 x = -3.717042675 + -3.4375 Combine like terms: -3.717042675 + -3.4375 = -7.154542675 x = -7.154542675 Simplifying x = -7.154542675Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.279542675, -7.154542675}
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