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Simplifying -1(2x + 11)(x + -2) = (2x + 11)(7x + -1) Reorder the terms: -1(11 + 2x)(x + -2) = (2x + 11)(7x + -1) Reorder the terms: -1(11 + 2x)(-2 + x) = (2x + 11)(7x + -1) Multiply (11 + 2x) * (-2 + x) -1(11(-2 + x) + 2x * (-2 + x)) = (2x + 11)(7x + -1) -1((-2 * 11 + x * 11) + 2x * (-2 + x)) = (2x + 11)(7x + -1) -1((-22 + 11x) + 2x * (-2 + x)) = (2x + 11)(7x + -1) -1(-22 + 11x + (-2 * 2x + x * 2x)) = (2x + 11)(7x + -1) -1(-22 + 11x + (-4x + 2x2)) = (2x + 11)(7x + -1) Combine like terms: 11x + -4x = 7x -1(-22 + 7x + 2x2) = (2x + 11)(7x + -1) (-22 * -1 + 7x * -1 + 2x2 * -1) = (2x + 11)(7x + -1) (22 + -7x + -2x2) = (2x + 11)(7x + -1) Reorder the terms: 22 + -7x + -2x2 = (11 + 2x)(7x + -1) Reorder the terms: 22 + -7x + -2x2 = (11 + 2x)(-1 + 7x) Multiply (11 + 2x) * (-1 + 7x) 22 + -7x + -2x2 = (11(-1 + 7x) + 2x * (-1 + 7x)) 22 + -7x + -2x2 = ((-1 * 11 + 7x * 11) + 2x * (-1 + 7x)) 22 + -7x + -2x2 = ((-11 + 77x) + 2x * (-1 + 7x)) 22 + -7x + -2x2 = (-11 + 77x + (-1 * 2x + 7x * 2x)) 22 + -7x + -2x2 = (-11 + 77x + (-2x + 14x2)) Combine like terms: 77x + -2x = 75x 22 + -7x + -2x2 = (-11 + 75x + 14x2) Solving 22 + -7x + -2x2 = -11 + 75x + 14x2 Solving for variable 'x'. Reorder the terms: 22 + 11 + -7x + -75x + -2x2 + -14x2 = -11 + 75x + 14x2 + 11 + -75x + -14x2 Combine like terms: 22 + 11 = 33 33 + -7x + -75x + -2x2 + -14x2 = -11 + 75x + 14x2 + 11 + -75x + -14x2 Combine like terms: -7x + -75x = -82x 33 + -82x + -2x2 + -14x2 = -11 + 75x + 14x2 + 11 + -75x + -14x2 Combine like terms: -2x2 + -14x2 = -16x2 33 + -82x + -16x2 = -11 + 75x + 14x2 + 11 + -75x + -14x2 Reorder the terms: 33 + -82x + -16x2 = -11 + 11 + 75x + -75x + 14x2 + -14x2 Combine like terms: -11 + 11 = 0 33 + -82x + -16x2 = 0 + 75x + -75x + 14x2 + -14x2 33 + -82x + -16x2 = 75x + -75x + 14x2 + -14x2 Combine like terms: 75x + -75x = 0 33 + -82x + -16x2 = 0 + 14x2 + -14x2 33 + -82x + -16x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 33 + -82x + -16x2 = 0 Factor a trinomial. (3 + -8x)(11 + 2x) = 0Subproblem 1
Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Subproblem 2
Set the factor '(11 + 2x)' equal to zero and attempt to solve: Simplifying 11 + 2x = 0 Solving 11 + 2x = 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 + 2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2x = 0 + -11 2x = 0 + -11 Combine like terms: 0 + -11 = -11 2x = -11 Divide each side by '2'. x = -5.5 Simplifying x = -5.5Solution
x = {0.375, -5.5}
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