4x^2+11x-69=0 Find the solution to use a comma to separate the answers as needed.

X^2+11x What is the constant term?(Integer or simplified fraction)

1/6 gt
y= (rationalize all Denominators)

4x^2+11x-69 = (x-3)(4x+23), so

x = -23/4,3

constant term is zero

??

To find the solution to the quadratic equation 4x^2 + 11x - 69 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 4, b = 11, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-11 ± √(11^2 - 4 * 4 * -69))/(2 * 4)

Simplifying further,

x = (-11 ± √(121 + 1104))/(8)

x = (-11 ± √1225)/(8)

Since the square root of 1225 is 35, we have:

x = (-11 ± 35)/(8)

This gives us two possible solutions for x:

x = (-11 + 35)/8 = 24/8 = 3

x = (-11 - 35)/8 = -46/8 = -5.75

So, the solutions to the equation 4x^2 + 11x - 69 = 0 are x = 3 and x = -5.75.

Moving on to the second part of the question, you mentioned x^2 + 11x, which does not seem to be related to the given equation. Could you please clarify or provide more information about what you are looking for?

Regarding the expression 1/6 gt, it appears to be an algebraic expression involving variables g and t. However, it is not clear what you are asking. Please provide more context or specify the question related to this expression.

Lastly, you mentioned "y = (rationalize all Denominators)." It seems that you are seeking an explanation regarding rationalizing denominators. Rationalizing denominators refers to the process of eliminating radicals (square roots or cube roots) from the denominator of a fraction.

To rationalize the denominator of a fraction like 1/y, where y has a radical in its denominator, you can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of y is y itself, so multiplying by y/y is equivalent to multiplying by 1 and does not change the value of the fraction. The numerator will remain the same, but when you multiply the denominators, the radical will be eliminated, resulting in a rationalized denominator.

For example, if you have the fraction 1/√2, you can rationalize the denominator by multiplying both numerator and denominator by √2:

(1/√2) * (√2/√2) = √2/2

So, the rationalized form of 1/√2 is √2/2.

Similarly, you can apply the same principle to rationalize denominators involving cube roots or higher roots. You multiply by the appropriate conjugate to eliminate the radical or root from the denominator.

If you have a specific fraction or expression that you would like to rationalize, please provide more details so that I can assist you further.