127k views
3 votes
Which of the following is a solution of 3x2 = 7x - 3?

Which of the following is a solution of 3x2 = 7x - 3?-example-1
User Jstacks
by
7.6k points

2 Answers

7 votes

we have


3x^(2)=7x-3

Group terms that contain the same variable, and move the constant to the opposite side of the equation


3x^(2)-7x=-3

Factor the leading coefficient


3(x^(2)-(7/3)x)=-3

Complete the square. Remember to balance the equation by adding the same constants to each side


3(x^(2)-(7/3)x+(49/36))=-3+(49/12)


3(x^(2)-(7/3)x+(49/36))=(13/12)

Rewrite as perfect squares


3(x-(7/6))^(2)=(13/12)


(x-(7/6))^(2)=(13/36)

square root both sides


x-(7)/(6)=(+/-) \sqrt{(13)/(36)}


x-(7)/(6)=(+/-) (√(13))/(6)


x=(7)/(6)(+/-) (√(13))/(6)

The solutions are


x=(7)/(6)+(√(13))/(6)=(-7+√(13))/(6)


x=(7)/(6)-(√(13))/(6)=(-7-√(13))/(6)

therefore

The answer is


x=(7\pm√(13))/(6)

User Nikolay Georgiev
by
8.4k points
5 votes
3x^2 = 7x - 3
3x^2 - 7x = -3
x^2 - 7/3x = -1
x^2 - 7/3x + 49/36 = -1 + 49/36 = 13/36
(x - 7/6)^2 = 13/36
x - 7/6 = + or - sqrt(13)/6
x = 7/6 + or - sqrt(13)/6
x = (7 + or - sqrt(13))/6

User Reznoir
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories