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Simplifying (9x + 2)(9x + -1) = x Reorder the terms: (2 + 9x)(9x + -1) = x Reorder the terms: (2 + 9x)(-1 + 9x) = x Multiply (2 + 9x) * (-1 + 9x) (2(-1 + 9x) + 9x * (-1 + 9x)) = x ((-1 * 2 + 9x * 2) + 9x * (-1 + 9x)) = x ((-2 + 18x) + 9x * (-1 + 9x)) = x (-2 + 18x + (-1 * 9x + 9x * 9x)) = x (-2 + 18x + (-9x + 81x2)) = x Combine like terms: 18x + -9x = 9x (-2 + 9x + 81x2) = x Solving -2 + 9x + 81x2 = x Solving for variable 'x'. Reorder the terms: -2 + 9x + -1x + 81x2 = x + -1x Combine like terms: 9x + -1x = 8x -2 + 8x + 81x2 = x + -1x Combine like terms: x + -1x = 0 -2 + 8x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.02469135802 + 0.0987654321x + x2 = 0 Move the constant term to the right: Add '0.02469135802' to each side of the equation. -0.02469135802 + 0.0987654321x + 0.02469135802 + x2 = 0 + 0.02469135802 Reorder the terms: -0.02469135802 + 0.02469135802 + 0.0987654321x + x2 = 0 + 0.02469135802 Combine like terms: -0.02469135802 + 0.02469135802 = 0.00000000000 0.00000000000 + 0.0987654321x + x2 = 0 + 0.02469135802 0.0987654321x + x2 = 0 + 0.02469135802 Combine like terms: 0 + 0.02469135802 = 0.02469135802 0.0987654321x + x2 = 0.02469135802 The x term is 0.0987654321x. Take half its coefficient (0.04938271605). Square it (0.002438652644) and add it to both sides. Add '0.002438652644' to each side of the equation. 0.0987654321x + 0.002438652644 + x2 = 0.02469135802 + 0.002438652644 Reorder the terms: 0.002438652644 + 0.0987654321x + x2 = 0.02469135802 + 0.002438652644 Combine like terms: 0.02469135802 + 0.002438652644 = 0.027130010664 0.002438652644 + 0.0987654321x + x2 = 0.027130010664 Factor a perfect square on the left side: (x + 0.04938271605)(x + 0.04938271605) = 0.027130010664 Calculate the square root of the right side: 0.164711902 Break this problem into two subproblems by setting (x + 0.04938271605) equal to 0.164711902 and -0.164711902.Subproblem 1
x + 0.04938271605 = 0.164711902 Simplifying x + 0.04938271605 = 0.164711902 Reorder the terms: 0.04938271605 + x = 0.164711902 Solving 0.04938271605 + x = 0.164711902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04938271605' to each side of the equation. 0.04938271605 + -0.04938271605 + x = 0.164711902 + -0.04938271605 Combine like terms: 0.04938271605 + -0.04938271605 = 0.00000000000 0.00000000000 + x = 0.164711902 + -0.04938271605 x = 0.164711902 + -0.04938271605 Combine like terms: 0.164711902 + -0.04938271605 = 0.11532918595 x = 0.11532918595 Simplifying x = 0.11532918595Subproblem 2
x + 0.04938271605 = -0.164711902 Simplifying x + 0.04938271605 = -0.164711902 Reorder the terms: 0.04938271605 + x = -0.164711902 Solving 0.04938271605 + x = -0.164711902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04938271605' to each side of the equation. 0.04938271605 + -0.04938271605 + x = -0.164711902 + -0.04938271605 Combine like terms: 0.04938271605 + -0.04938271605 = 0.00000000000 0.00000000000 + x = -0.164711902 + -0.04938271605 x = -0.164711902 + -0.04938271605 Combine like terms: -0.164711902 + -0.04938271605 = -0.21409461805 x = -0.21409461805 Simplifying x = -0.21409461805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.11532918595, -0.21409461805}
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