Question

1-36. George was solving the equation (2x-1)(x+3)=4 and he got the solutions x=12 and x=-3.Jeffrey came along and said, “You made a big mistake! You set each factor equal to zero, but it'snot equal to zero, it's equal to 4. So you have to set each factor equal to 4 and then solve." Who iscorrect? Show George and Jeffrey how to solve this equation. To be sure that you are correct,check your solutions. Homework Help

Answer 1

The solutions are -7/2 and 1. Jeffrey is correct.

Explanation:

We have to use the Bhaskara formula to solve this question.

Bhaskara formula:

Suppose we have the following second order equation:

ax² + bx + c = 0

The solution of the equation are:

`x=(-b\pm√(b^2-4ac))/(2a)`

In this question:

(2x - 1)(x + 3) = 4

We have to apply the distributive property to place the equation in the correct format to apply Bhaskara.

(2x - 1)(x + 3) = 4

2x² + 6x - x - 3 = 4

2x² + 5x - 3 - 4 = 0

2x² + 5x - 7 = 0

`x=(-5\pm√((5)^2-4\ast2\ast(-7)))/(2\ast2)=(-5\pm√(25+56))/(4)=(-5\pm√(81))/(4)=(-5\pm9)/(4)`

The solutions are:

`x^{^(\prime)}=(-5+9)/(4)=1`
`x^{^(\prime\prime)}=(-5-9)/(4)=-(14)/(4)=-(7)/(2)`

The solutions are -7/2 and 1. Jeffrey is correct.