3q^2=2q+8 use qaudratic formula and solve
please solve this in a book and give me the answer
Answers
Answer:
How to solve your problem
32=2+8
3q^{2}=2q+83q2=2q+8
Quadratic formula
Factor
1
Move terms to the left side
32=2+8
3q^{2}=2q+83q2=2q+8
32−(2+8)=0
3q^{2}-\left(2q+8\right)=03q2−(2q+8)=0
2
Distribute
32−(2+8)=0
3q^{2}-\left(2q+8\right)=03q2−(2q+8)=0
32−2−8=0
3q^{2}-2q-8=03q2−2q−8=0
3
Use the quadratic formula
=−±2−4√2
q=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}q=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
32−2−8=0
3q^{2}-2q-8=03q2−2q−8=0
=3
a={\color{#c92786}{3}}a=3
=−2
b={\color{#e8710a}{-2}}b=−2
=−8
c={\color{#129eaf}{-8}}c=−8
=−(−2)±(−2)2−4⋅3(−8)√2⋅3
q=\frac{-({\color{#e8710a}{-2}}) \pm \sqrt{({\color{#e8710a}{-2}})^{2}-4 \cdot {\color{#c92786}{3}}({\color{#129eaf}{-8}})}}{2 \cdot {\color{#c92786}{3}}}q=2⋅3−(−2)±(−2)2−4⋅3(−8)
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Answer:
Solution
=
2
=
−
4
3
Step-by-step explanation:
1
Move terms to the left side
3
2x
=
2
+
8
3q^{2}=2q+8
3q2=2q+8
3
2
−
(
2
+
8
)
=
0
3q^{2}-\left(2q+8\right)=0
3q2−(2q+8)=0
2
Distribute
3
Use the quadratic formula
4
Simplify
5
Separate the equations
6
and you can refer to this too :-
Correct :-
q=2,
3
−4
Given equation is,
3q
2
=2q+8
3q
2
−2q−8=0
3q
2
−6q+4q−8=0
3q(q−2)+4(q−2)=8
(3q+4)(q−2)=0
∴q=2,
3
−4
∴ roots of the given equation are 2,
3
−4
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