Answer:
Step-by-step 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)
Answer:
x = - 2, x = [tex]\frac{3}{2}[/tex]
Step-by-step 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 = [tex]\frac{3}{2}[/tex]
