Answer to Question #153597 in Algebra for Rajanikanth R

Question

To solve the equation 5x^2+x-4=2 , you should start by factoring the left side as (5x-4)(x+1). Is the statement correct? Explain in detail. Show how to solve the equation without the use of the quadratic formula.

Answer 1

Ideally, the general form of a quadratic equation is ax² + bx + c = 0 so the equation has to be re-written as 5x² + x -6 =0

We are going to factorise using the factorization method:

From ax² + bx + c = 0

ax² multiplied by c = acx²

Then find two numbers so that if you multiply will give acx² and if you add will give bx.

Using the given equation: 5x² + x -6 =0

5x² * -6 = -30x²

So we need to find two numbers so such if we multiply will give -30x² and if we add will give +x

This leaves us with +6x and -5x

Input (+6x -5x) in place of +x

5x² +6x -5x -6 =0

Factorise what term is common

x(5x +6) -1(5x+6) =0

For you to be correct, the terms in the bracket must be the same.

(x-1)(5x+6) =0

Equate each into 0

x-1 =0 or 5x+6 =0

Therefore, x = 1 or x = -6/5