Question

Solve the equation by factoring 2x^2+x-6=0

Answer 1

x = - 2, x =
`(3)/(2)`

Explanation:

Given

2x² + x - 6 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 6 = - 12 and sum = + 1

The factors are + 4 and - 3

Use these factors to split the x- term

2x² + 4x - 3x - 6 = 0 ( factor the firs/second and third/fourth terms )

2x(x + 2) - 3(x + 2) = 0 ← factor out (x + 2) from each term

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

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
`(3)/(2)`

Answer 2

Explanation:

Use the quadratic formula

=

−

±

2

−

4

√

2

x

=

−

b

±

b

2

−

4

a

c

2

a

x=2a−b±b2−4ac​​

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

2

2

+

−

6

=

0

2

x

2

+

x

−

6

=

0

2x2+x−6=0

=

2

a

=

2

a=2

=

1

b

=

1

b=1

=

−

6

c

=

−

6

c=−6

=

−

1

±

1

2

−

4

⋅

2

(

−

6

)

√

2

⋅

2

x

=

−

1

±

1

2

−

4

⋅

2

(

−

6

)

2

⋅

2

x=2⋅2−1±12−4⋅2(−6)​​