3x^2 + 7x- 31 = 0 i think you can solve it by completing the square, my textbook is giving horrible examples

Answer 1

ok if u want to solve it by using completing square its like this

3x^2+7x-31 = 0

take 3 out

3(x^2+(7/3)x-(31/3)) = 0
get rid of 3

so u get

x^2+(7/3)x-(31/3) = 0

By completing square method
1st divide (7/3) by 2,add to x and complete square and substract the constant from it
(x+(7/6))^2 -(49/36 =0

(x+(7/6))^2 -(49/36) = 31/3
(x+(7/6))^2 =31/3+49/36

x+(7/6) = +or-root(11.6944)
x = 2.25304 or x =-4.58637


So the answers are x = 2.25304 or x =-4.58637 by using thecompleting square method

U can do easily by using the formula -b+or- root(b^2-4ac)2a equation and obtain the same answer.

Answer 2

3x^2 + 7x - 31 = 0
x^2 + 7/3x - 31/3 = 0
Got rid of the coefficient 3 by dividing it with all the other terms.

x^2 + 7/3x = 31/3
Added 31/3 on both sides

x^2 + 7/3x + 49/36 = 31/3 + 49/36
Found the third term by dividing the second term by 2 then squaring it and added it to both sides of the equation.

(x + 7/6)^2 = 372/36 Factored the left side of the equation

Then you find the square root for both sides, the term on the right side of the equation has a plus minus sign in front of it and then u rationalize the denominator. You should end up with x + 7/6 = +/- Radical 372 over 6.

Subtract 7/6 on both sides and simplify the radical. I ended up with x = -7/6 +/- 2 radical 93 over 6

I could be wrong and I might've lost u at one point there, I'm sorry if I did..I tried, hope it helps..somehow..

Answer 3

3x^2 + 7x- 31 = 0
3(x^2+7x/3+49/36)-31-49/12=0
3(x+7/6)^2=31+49*12
(x+7/6)^2=(372+49)/36
(x+7/6)^2=421/36
x+7/6=+/-√(421) /6
x=(-7+/-√(421))/6

Answer 4

3x^2+7x-31=0

(-7+ SQR (49+372)) /6 = 2.253
(-7- SQR (49+372)) /6 = -4.586
If you will check you will find this is the correct answer

Answer 5

Use the quadratic formula.

x= -b (+ or -) the square root of b^2 -4ac all over 2a

Answer 6

use quadratic formula

(-b+sqrt(4ac))/2a and (-b-sqrt(4ac))/2a

so it would be (-7+sqrt(4*3*31))/2*3 and (-7-sqrt(4*3*31))/2*3

those are the 2 solutions for x

Answer 7

3x^2 + 7x - 31 = 0

a=3, b=7, c=-31

x = (-b+sqrt(b^2-4ac))/2a or (-b-sqrt(b^2-4ac))/2a
x = (-7+sqrt(7^2-4*3*(-31)))/(2*3) or (-7-sqrt(7^2-4*3*(-31)))/(2*3)
x = (-7+sqrt(421))/6 or (-7-sqrt(421))/6
x = 2.25 or -4.59

Answer 8

I'd suggest using quadratic formula.
(-b+/-sqrt(b^2-4ac))/2a
(-7+/-sqrt(7^2-4*3*(-31)))/(2*3)
(-7+/-sqrt(421))/6
(-7+sqrt(421))/6 or (-7-sqrt(421))/6
about 2.530 or -4.586