Solve the quadratic by factoring.6, x, squared, plus, 4, x, plus, 1, equals, 9, x6x 2 +4x+1=9x

First, let's rewrite the equation to have all terms on one side:

6x^2 + 4x - 9x + 1 = 0

This simplifies to:

6x^2 - 5x + 1 = 0

Now, we need to factor this quadratic equation. However, this equation does not factor nicely with integer values. Therefore, we will need to use the quadratic formula to solve for x. The quadratic formula is:

x = [-b ± sqrt(b^2 - 4ac)] / (2a)

In this equation, a = 6, b = -5, and c = 1. Plugging these values into the quadratic formula gives:

x = [5 ± sqrt((-5)^2 - 461)] / (2*6) x = [5 ± sqrt(25 - 24)] / 12 x = [5 ± sqrt(1)] / 12

So the solutions are:

x = (5 + 1) / 12 = 0.5 x = (5 - 1) / 12 = 0.333...