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Simplifying (35x + 1)(4x + 7) = -1(19x + 44) Reorder the terms: (1 + 35x)(4x + 7) = -1(19x + 44) Reorder the terms: (1 + 35x)(7 + 4x) = -1(19x + 44) Multiply (1 + 35x) * (7 + 4x) (1(7 + 4x) + 35x * (7 + 4x)) = -1(19x + 44) ((7 * 1 + 4x * 1) + 35x * (7 + 4x)) = -1(19x + 44) ((7 + 4x) + 35x * (7 + 4x)) = -1(19x + 44) (7 + 4x + (7 * 35x + 4x * 35x)) = -1(19x + 44) (7 + 4x + (245x + 140x2)) = -1(19x + 44) Combine like terms: 4x + 245x = 249x (7 + 249x + 140x2) = -1(19x + 44) Reorder the terms: 7 + 249x + 140x2 = -1(44 + 19x) 7 + 249x + 140x2 = (44 * -1 + 19x * -1) 7 + 249x + 140x2 = (-44 + -19x) Solving 7 + 249x + 140x2 = -44 + -19x Solving for variable 'x'. Reorder the terms: 7 + 44 + 249x + 19x + 140x2 = -44 + -19x + 44 + 19x Combine like terms: 7 + 44 = 51 51 + 249x + 19x + 140x2 = -44 + -19x + 44 + 19x Combine like terms: 249x + 19x = 268x 51 + 268x + 140x2 = -44 + -19x + 44 + 19x Reorder the terms: 51 + 268x + 140x2 = -44 + 44 + -19x + 19x Combine like terms: -44 + 44 = 0 51 + 268x + 140x2 = 0 + -19x + 19x 51 + 268x + 140x2 = -19x + 19x Combine like terms: -19x + 19x = 0 51 + 268x + 140x2 = 0 Factor a trinomial. (17 + 10x)(3 + 14x) = 0Subproblem 1
Set the factor '(17 + 10x)' equal to zero and attempt to solve: Simplifying 17 + 10x = 0 Solving 17 + 10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 10x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 10x = 0 + -17 10x = 0 + -17 Combine like terms: 0 + -17 = -17 10x = -17 Divide each side by '10'. x = -1.7 Simplifying x = -1.7Subproblem 2
Set the factor '(3 + 14x)' equal to zero and attempt to solve: Simplifying 3 + 14x = 0 Solving 3 + 14x = 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 + 14x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 14x = 0 + -3 14x = 0 + -3 Combine like terms: 0 + -3 = -3 14x = -3 Divide each side by '14'. x = -0.2142857143 Simplifying x = -0.2142857143Solution
x = {-1.7, -0.2142857143}
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