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Simplifying (4x + 1)(4x + 1) + 9(4x + 1) = -18 Reorder the terms: (1 + 4x)(4x + 1) + 9(4x + 1) = -18 Reorder the terms: (1 + 4x)(1 + 4x) + 9(4x + 1) = -18 Multiply (1 + 4x) * (1 + 4x) (1(1 + 4x) + 4x * (1 + 4x)) + 9(4x + 1) = -18 ((1 * 1 + 4x * 1) + 4x * (1 + 4x)) + 9(4x + 1) = -18 ((1 + 4x) + 4x * (1 + 4x)) + 9(4x + 1) = -18 (1 + 4x + (1 * 4x + 4x * 4x)) + 9(4x + 1) = -18 (1 + 4x + (4x + 16x2)) + 9(4x + 1) = -18 Combine like terms: 4x + 4x = 8x (1 + 8x + 16x2) + 9(4x + 1) = -18 Reorder the terms: 1 + 8x + 16x2 + 9(1 + 4x) = -18 1 + 8x + 16x2 + (1 * 9 + 4x * 9) = -18 1 + 8x + 16x2 + (9 + 36x) = -18 Reorder the terms: 1 + 9 + 8x + 36x + 16x2 = -18 Combine like terms: 1 + 9 = 10 10 + 8x + 36x + 16x2 = -18 Combine like terms: 8x + 36x = 44x 10 + 44x + 16x2 = -18 Solving 10 + 44x + 16x2 = -18 Solving for variable 'x'. Reorder the terms: 10 + 18 + 44x + 16x2 = -18 + 18 Combine like terms: 10 + 18 = 28 28 + 44x + 16x2 = -18 + 18 Combine like terms: -18 + 18 = 0 28 + 44x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + 11x + 4x2) = 0 Factor a trinomial. 4((7 + 4x)(1 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1.75, -1}
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