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# Solve the quadratic equations where possible? watch

1. 5x^2+9x+3=0 and 2x^2+x-7=0

you can't factorise these, how do i solve this non calculator?
2. (Original post by tom989)
5x^2+9x+3=0 and 2x^2+x-7=0

you can't factorise these, how do i solve this non calculator?
What other methods do you know for solving quadratics?
Spoiler:
Show
It involves a formula.
4. (Original post by SeanFM)
What other methods do you know for solving quadratics?
Spoiler:
Show
It involves a formula.
Spoiler:
Show
Or complete the square.
5. how would i use complete the square?
6. (Original post by tom989)
Correct. But you can take your pick between that and the other method suggested
7. (Original post by tom989)
how would i use complete the square?
Let's use a general formula:
Step 1 - take a out of the terms involving x:
Step 2 - look at the divide through by x and divide the second term by 2 (and square the bracket):
Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
8. there are 4 ways to solve quadratics:
1. Complete the square
3. factorise
4. graphs (yes you can use graphs to use quadratic)

You're best choices will be the formula (you find it online) and graphs (but you'll have to use excel to ensure that you get an accurate answer) - input some numbers in the formula and plot an XY scatter graph in excel and take interception of the shape with X line ... it should work very well
9. (Original post by RAlexO)
there are 4 ways to solve quadratics:
1. Complete the square
3. factorise
4. graphs (yes you can use graphs to use quadratic)

You're best choices will be the formula (you find it online) and graphs (but you'll have to use excel to ensure that you get an accurate answer) - input some numbers in the formula and plot an XY scatter graph in excel and take interception of the shape with X line ... it should work very well
You'll rarely get a precise answer solving them graphically, If you include that then you have to include numerical methods as well.
Also, they're unlikely to be allowed to use Excel in their exam.
10. (Original post by morgan8002)
You'll rarely get a precise answer solving them graphically, If you include that then you have to include numerical methods as well.
Also, they're unlikely to be allowed to use Excel in their exam.
I did not know he needed it for an exam... I thought it is some sort of homework or essay .
11. (Original post by Andy98)
Let's use a general formula:
Step 1 - take a out of the terms involving x:
Step 2 - look at the divide through by x and divide the second term by 2 (and square the bracket):
Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
12. (Original post by Zacken)
Oh yeah, oops
13. (Original post by Andy98)
Oh yeah, oops
Which is, by the way, precisely how you derive the quadratic formula.
14. (Original post by Zacken)
Which is, by the way, precisely how you derive the quadratic formula.
It is?
15. (Original post by Andy98)
It is?

So, isolating 'x':

Square rooting and isolating x:

16. (Original post by Zacken)

So, isolating 'x':

Square rooting and isolating x:

Wow! I never realised that. Nice!
17. (Original post by Andy98)
Wow! I never realised that. Nice!
Learn something new everyday.
18. (Original post by Zacken)
Learn something new everyday.
True
19. (Original post by Andy98)
Let's use a general formula:
Step 1 - take a out of the terms involving x:
Step 2 - look at the divide through by x and divide the second term by 2 (and square the bracket):
Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
You have to account for the extra term when the bracket is squared by subtracting (b^2)/4a^2, so in the case of 5x^2 + 9x + 3 = 0 you get:

5[x^2 + 1.8x + 0.6] = 0
X^2 + 1.8x + 0.6 = 0
(X + 0.9)^2 + 0.6 - 0.81 = 0
(X + 0.9)^2 - 0.21 = 0
(X + 0.9)^2 = 0.21
X + 0.9 = +/- sqrt(0.21)
∴ x = -0.9 +/- sqrt(0.21)
20. (Original post by vectorpi)
You have to account for the extra term when the bracket is squared by subtracting (b^2)/4a^2, so in the case of 5x^2 + 9x + 3 = 0 you get:

5[x^2 + 1.8x + 0.6] = 0
X^2 + 1.8x + 0.6 = 0
(X + 0.9)^2 + 0.6 - 0.81 = 0
(X + 0.9)^2 - 0.21 = 0
(X + 0.9)^2 = 0.21
X + 0.9 = +/- sqrt(0.21)
∴ x = -0.9 +/- sqrt(0.21)

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