Question

Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.

Answer 1

Hello,

6x²-5x-56=0
==>6x²-21x+16x-56=0
==>3x(2x-7)+8(2x-7)=0
==>(2x-7)(3x+8)=0
==>x=7/2 or x= -8/3

Answer 2

Consider the given equation $6x^2-5x=56$

We have to use the zero product property to evaluate the solutions to the given equation.

The Zero product property states that "The product of factors is zero if and only if one or more of the factors is zero".

Since, $6x^2-5x=56$

$6x^2-5x-56=0$

We will use "middle the splitting term" method to evaluate its solutions.

$6x^2-5x-56=0$

$6x^2-21x+16x-56=0$

$3x(2x-7)+8(2x-7)=0$

$(3x+8)(2x-7)=0$

Now, by zero product property,

$3x+8=0$

$x=\frac{-8}{3}$

or

$2x-7=0$

$x=\frac{7}{2}$

So, the solutions are $x=\frac{-8}{3}$ or $x=\frac{7}{2}$.