Verified answer

Its your choice on which solution you will use.

i will show you 2 ways (factoring and completing square)

FACTORING:

2x^2 + x = 6

2x^2 + x - 6 = 0

(2x -3)(x + 2 ) = 0

ans:

x = 3/2

x = -2

COMPLETING THE SQUARE:

2x^2 + x = 6

x^2 + (1/2)x = 3

x^2 + (1/2)x + 1/16 = 3 + 1/16

(x + 1/4) ^ 2 = 49/16

x + 1/4 = +/- 7/4

==> x = 7/4 -1/4

==> x = -7/4 -1/4

ans.

x = 3/2

x = -2

you now decide which is easier for you.

note: i cant show you how to solve it by graph.

Graphing is the basic method in solving any problem like this

but the problem is it take a long time to solve problem also it need some accurate to get best answer

(Useally we use computer to draw the gragh for us)

Factoring It is a comman that we use because it safes our time also it give us what we need

But the problem we had is that if factor is wrong way it well give us a wrong answer

Finally

I well choose completing the square method to safe my time in solving this question ( using quarfinatic formula)

Soluation:

2x^2 + x = 6

2x^2 + x - 6 = 0

let a = 2 , b = 1 , c = -6

x1,2 = [-b (+ or -) (b^2 - 4ac)^1/2] / 2a

x1 = [-1 + (1^2 - 4(2)(-6))^1/2] / 2(2)

x1 = [ -1 (+7)] / 4

x1 = 6 / 4

x1 = 3 / 2

x2 = [-1 - (1^2 - 4(2)(-6))^1/2] / 2(2)

x2 = [-1 (- 7) / 4

x2 = -8 / 4

x2 = -4 / 2

x2 = - 2

therefor

x has to values for this problem they are

x1 = 3/2

x2 = -2

factoring, because you can factor the equation:

2x^2 + x - 6 = 0 when you solve that equation.

(x+2)(2x-3) = 0

Answers:

x = -2

x = 3/2

Factoring because it is easier to find the roots this way, , ,

2x^2 + x - 6 = 0

2x^2 + 4x - 3x - 6 = 0

2x (x + 2) - 3 (x + 2) = 0

(x + 2)(2x - 3) = 0

x = -2

x = 3/2

(2x - 3)(x + 2) = 0

Try factoring first.

graphing, its basically always the easiest method