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Simplifying (5x + 4)(5x + 4) + 6(5x + 4) = 7 Reorder the terms: (4 + 5x)(5x + 4) + 6(5x + 4) = 7 Reorder the terms: (4 + 5x)(4 + 5x) + 6(5x + 4) = 7 Multiply (4 + 5x) * (4 + 5x) (4(4 + 5x) + 5x * (4 + 5x)) + 6(5x + 4) = 7 ((4 * 4 + 5x * 4) + 5x * (4 + 5x)) + 6(5x + 4) = 7 ((16 + 20x) + 5x * (4 + 5x)) + 6(5x + 4) = 7 (16 + 20x + (4 * 5x + 5x * 5x)) + 6(5x + 4) = 7 (16 + 20x + (20x + 25x2)) + 6(5x + 4) = 7 Combine like terms: 20x + 20x = 40x (16 + 40x + 25x2) + 6(5x + 4) = 7 Reorder the terms: 16 + 40x + 25x2 + 6(4 + 5x) = 7 16 + 40x + 25x2 + (4 * 6 + 5x * 6) = 7 16 + 40x + 25x2 + (24 + 30x) = 7 Reorder the terms: 16 + 24 + 40x + 30x + 25x2 = 7 Combine like terms: 16 + 24 = 40 40 + 40x + 30x + 25x2 = 7 Combine like terms: 40x + 30x = 70x 40 + 70x + 25x2 = 7 Solving 40 + 70x + 25x2 = 7 Solving for variable 'x'. Reorder the terms: 40 + -7 + 70x + 25x2 = 7 + -7 Combine like terms: 40 + -7 = 33 33 + 70x + 25x2 = 7 + -7 Combine like terms: 7 + -7 = 0 33 + 70x + 25x2 = 0 Factor a trinomial. (11 + 5x)(3 + 5x) = 0Subproblem 1
Set the factor '(11 + 5x)' equal to zero and attempt to solve: Simplifying 11 + 5x = 0 Solving 11 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 5x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 5x = 0 + -11 5x = 0 + -11 Combine like terms: 0 + -11 = -11 5x = -11 Divide each side by '5'. x = -2.2 Simplifying x = -2.2Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Solution
x = {-2.2, -0.6}
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