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Simplifying (4x + 1)(4x + 1) = x + 10 Reorder the terms: (1 + 4x)(4x + 1) = x + 10 Reorder the terms: (1 + 4x)(1 + 4x) = x + 10 Multiply (1 + 4x) * (1 + 4x) (1(1 + 4x) + 4x * (1 + 4x)) = x + 10 ((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = x + 10 ((1 + 4x) + 4x * (1 + 4x)) = x + 10 (1 + 4x + (1 * 4x + 4x * 4x)) = x + 10 (1 + 4x + (4x + 16x2)) = x + 10 Combine like terms: 4x + 4x = 8x (1 + 8x + 16x2) = x + 10 Reorder the terms: 1 + 8x + 16x2 = 10 + x Solving 1 + 8x + 16x2 = 10 + x Solving for variable 'x'. Reorder the terms: 1 + -10 + 8x + -1x + 16x2 = 10 + x + -10 + -1x Combine like terms: 1 + -10 = -9 -9 + 8x + -1x + 16x2 = 10 + x + -10 + -1x Combine like terms: 8x + -1x = 7x -9 + 7x + 16x2 = 10 + x + -10 + -1x Reorder the terms: -9 + 7x + 16x2 = 10 + -10 + x + -1x Combine like terms: 10 + -10 = 0 -9 + 7x + 16x2 = 0 + x + -1x -9 + 7x + 16x2 = x + -1x Combine like terms: x + -1x = 0 -9 + 7x + 16x2 = 0 Factor a trinomial. (-1 + -1x)(9 + -16x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(9 + -16x)' equal to zero and attempt to solve: Simplifying 9 + -16x = 0 Solving 9 + -16x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -16x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16x = 0 + -9 -16x = 0 + -9 Combine like terms: 0 + -9 = -9 -16x = -9 Divide each side by '-16'. x = 0.5625 Simplifying x = 0.5625Solution
x = {-1, 0.5625}
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