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Simplifying 6(x + 9)(x + 9) + -23(x + 9) = 4 Reorder the terms: 6(9 + x)(x + 9) + -23(x + 9) = 4 Reorder the terms: 6(9 + x)(9 + x) + -23(x + 9) = 4 Multiply (9 + x) * (9 + x) 6(9(9 + x) + x(9 + x)) + -23(x + 9) = 4 6((9 * 9 + x * 9) + x(9 + x)) + -23(x + 9) = 4 6((81 + 9x) + x(9 + x)) + -23(x + 9) = 4 6(81 + 9x + (9 * x + x * x)) + -23(x + 9) = 4 6(81 + 9x + (9x + x2)) + -23(x + 9) = 4 Combine like terms: 9x + 9x = 18x 6(81 + 18x + x2) + -23(x + 9) = 4 (81 * 6 + 18x * 6 + x2 * 6) + -23(x + 9) = 4 (486 + 108x + 6x2) + -23(x + 9) = 4 Reorder the terms: 486 + 108x + 6x2 + -23(9 + x) = 4 486 + 108x + 6x2 + (9 * -23 + x * -23) = 4 486 + 108x + 6x2 + (-207 + -23x) = 4 Reorder the terms: 486 + -207 + 108x + -23x + 6x2 = 4 Combine like terms: 486 + -207 = 279 279 + 108x + -23x + 6x2 = 4 Combine like terms: 108x + -23x = 85x 279 + 85x + 6x2 = 4 Solving 279 + 85x + 6x2 = 4 Solving for variable 'x'. Reorder the terms: 279 + -4 + 85x + 6x2 = 4 + -4 Combine like terms: 279 + -4 = 275 275 + 85x + 6x2 = 4 + -4 Combine like terms: 4 + -4 = 0 275 + 85x + 6x2 = 0 Factor a trinomial. (55 + 6x)(5 + x) = 0Subproblem 1
Set the factor '(55 + 6x)' equal to zero and attempt to solve: Simplifying 55 + 6x = 0 Solving 55 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + 6x = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 6x = 0 + -55 6x = 0 + -55 Combine like terms: 0 + -55 = -55 6x = -55 Divide each side by '6'. x = -9.166666667 Simplifying x = -9.166666667Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-9.166666667, -5}
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