Final answer:
To solve the equation 25x²-36, factor it as a difference of squares into (5x+6)(5x-6)=0, and solve for x to get the solutions x=-6/5 and x=6/5. The quadratic formula is an alternative method suitable for more complex quadratic equations.
Step-by-step explanation:
To solve the equation 25x²-36, first note that this is a difference of squares, as 25x² is (5x)² and 36 is 6². The difference of squares factoring is applied to get (5x+6)(5x-6) = 0. From here, each factor can be set to zero to find the solutions for x.
The equation (5x+6)(5x-6) = 0 leads us to two potential solutions. If 5x+6=0, then x=-6/5; and if 5x-6=0, then x=6/5. These are the two solutions for the equation 25x²-36=0.
If this were a more complex quadratic, such as x²+1.2 x 10-2x -6.0 × 10-³ = 0, we could use the quadratic formula to solve for x, which is necessary when the equation does not simplify into a perfect square or a factorable form.