Solve Quadratic Equation: 5x^2 - 16tx + 3t^2

[Atomised]

Homework Statement

Solve 5x^2 - 16tx + 3t^2 for x without using quadratic formula.

I am interested in understanding the technique - I have the answers already: t/5, 3t

Homework Equations

I have solved the subsequent question which is:

tx^2 + (tT - 1)x - T = 0, which seems easier because it breaks into four clusters which can be factored, then refactored and solved. The one I am asking about does not seem amenable to the same approach, or any other that I know.

The Attempt at a Solution

I am interested in higher maths but having to mend holes in elementary technique. Thanks in advance.

 

[mpittma1]

Homework Statement

Solve 5x^2 - 16tx + 3t^2 for x without using quadratic formula.

I am interested in understanding the technique - I have the answers already: t/5, 3t

Homework Equations

I have solved the subsequent question which is:

tx^2 + (tT - 1)x - T = 0, which seems easier because it breaks into four clusters which can be factored, then refactored and solved. The one I am asking about does not seem amenable to the same approach, or any other that I know.

The Attempt at a Solution

I am interested in higher maths but having to mend holes in elementary technique. Thanks in advance.

is the whole equation 5x^2 - 16tx + 3t^2=0?

 

[scurty]

Since 5 and 3 are both prime, you only have 4 different possibilities of how the terms appear when you use the factor method. Perhaps the variable t is throwing you off? Start by letting t = 1 just so it's clearer to you and then go back and solve the equation with t.

Also, you can only solve for a variable if you have an equation. The original expression must be set equal to 0.

 

[Atomised]

Yes - the only other info stated in the question is 'Express x in terms of the other letters'.

 

[Atomised]

Ah apologies - I have only stated the LHS, the equation is

5x^2 - 16tx + 3t^2=0

 

[Atomised]

Thank you Scurty, the t was throwing me.

(5x - t) (x - 3t)