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Simplifying (4x + 1)(x + -9) + -8 = 0 Reorder the terms: (1 + 4x)(x + -9) + -8 = 0 Reorder the terms: (1 + 4x)(-9 + x) + -8 = 0 Multiply (1 + 4x) * (-9 + x) (1(-9 + x) + 4x * (-9 + x)) + -8 = 0 ((-9 * 1 + x * 1) + 4x * (-9 + x)) + -8 = 0 ((-9 + 1x) + 4x * (-9 + x)) + -8 = 0 (-9 + 1x + (-9 * 4x + x * 4x)) + -8 = 0 (-9 + 1x + (-36x + 4x2)) + -8 = 0 Combine like terms: 1x + -36x = -35x (-9 + -35x + 4x2) + -8 = 0 Reorder the terms: -9 + -8 + -35x + 4x2 = 0 Combine like terms: -9 + -8 = -17 -17 + -35x + 4x2 = 0 Solving -17 + -35x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -8.75x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -8.75x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -8.75x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -8.75x + x2 = 0 + 4.25 -8.75x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -8.75x + x2 = 4.25 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = 4.25 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 4.25 + 19.140625 Combine like terms: 4.25 + 19.140625 = 23.390625 19.140625 + -8.75x + x2 = 23.390625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 23.390625 Calculate the square root of the right side: 4.836385531 Break this problem into two subproblems by setting (x + -4.375) equal to 4.836385531 and -4.836385531.Subproblem 1
x + -4.375 = 4.836385531 Simplifying x + -4.375 = 4.836385531 Reorder the terms: -4.375 + x = 4.836385531 Solving -4.375 + x = 4.836385531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 4.836385531 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 4.836385531 + 4.375 x = 4.836385531 + 4.375 Combine like terms: 4.836385531 + 4.375 = 9.211385531 x = 9.211385531 Simplifying x = 9.211385531Subproblem 2
x + -4.375 = -4.836385531 Simplifying x + -4.375 = -4.836385531 Reorder the terms: -4.375 + x = -4.836385531 Solving -4.375 + x = -4.836385531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -4.836385531 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -4.836385531 + 4.375 x = -4.836385531 + 4.375 Combine like terms: -4.836385531 + 4.375 = -0.461385531 x = -0.461385531 Simplifying x = -0.461385531Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.211385531, -0.461385531}
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