Algebra 2 my friends! Does anyone know anything about quadratic equations??? 
Plenty. 
What in particular would you like to know? I’m sure I could help.
oh gosh thanks 
quadratics… factoring… squareroots…
It’s all pretty confusing, but can you explain how to do this problem step by step?
x ² -6x-7=0
and maybe… If it’s not too much trouble ^^;
6x ²+9=-55x
Just let me know if this isn’t clear, sometimes I find it hard to write out solutions without a proper equation editor.
So, let’s suppose we wish to use factorisation to solve the following equation:
x ² -6x-7=0
Factorisation is basically the process by which we convert this equation to one of the form:
a(x + b) ² + c = 0
→ ax ² + 2abx + ab ² + c = 0
Now, in this case, we can immediate see that a = 1 (compare ax ² to x ² in your equation), so we want to turn x ² – 6x – 7 = 0 into
x ² + 2bx + b ² + c = 0
Again, by comparison with x ² – 6x – 7 = 0, b = -3 (compare – 6x with 2bx). Hence, b ² = 9. Finally, this must mean that c = -16, since -7 = b ² + c = 9 + c.
So, x ² – 6x – 7 = x ² – 6x + 9 – 16 = (x – 3) ² – 16 = 0
→ (x – 3) ² = 16
→ x – 3 = +/- 4
Careful! There are two solutions here for x. This is because I’ve taken the square root of both sides. Now, the square root of 16 may be either 4 or -4, since the square of 4 is 16, and the square of -4 is also 16. Hence, x - 3 may be either 4 or -4.
→ x = 3 + 4 = 7 or x = 3 – 4 = -1
Okay, so that’s the first equation out of the way with - x may be either 7 or -1. Try substituting these back into the original equation to make sure you get zero. Now let’s try equation 2:
6x ²+9=-55x
Rewrite this so that all the terms are on the left hand side:
6x ² + 55x + 9 = 0
Again, comparing this to ax ² + 2abx + ab ² + c = 0, and we can see that a = 6. Also, 2ab = 55, so 2(6)b = 55 → b = 55/12. Finally, 6 (55/12) ² + c = 9, so c = 9 – 6 (55/12) ²
Hence,
6x ² + 55x + 9 = 6x ² + 55x + 6(55/12) ² – 6(55/12) ² + 9 = 6(x + 55/12) ² – 6(55/12) ² + 9 = 0
→ 6(x + 55/12) ² = [6(55) ² – 9*144]/144
(X + 55/12) ² = [(55) ² – 3*72]/144 = 2809/144
X + 55/12 = +/- 53/12
X = -55/12 +/- 53/12
So, = [-55 +/- 53]/12
= (-55 – 53)/12 or (-55 + 53)/12
Ie. x = - 9 or -1/6
By the way, there is an easy way you can solve these types of problems without resorting to factorisation. Suppose we have a quadratic equation of the form:
ax ² + bx + c = 0
Then, the generic quadratic formula for roots (ie. the points where the quadratic intersect the x-axis) is given by
x = [- b +/- √(b ² - 4ac)] / 2a
(there may be a maximum of two solutions, corresponding to + and -)
So! Your first quadratic equation is:
x ² -6x-7=0
So, a = 1, b = -6, c = -7
Substitute those into the quadratic formula for the roots;
x = [6 +/- √(36 + 28 )]/2
= [6 +/- √(64)]/2
= [6 +/- 8]/2
= [6 + 8]/2 or [6 – 8]/2
So you have two solutions to the quadratic equation, 7 and -1. Fantastic - this corresponds to the solution we found earlier. Let’s check the second equation;
6x ²+9=-55x, so a = 6, b = 55, c = 9
X = [-55 +/- √(55^2 – 469)]/12
= [-55 +/- 53]/12
= (-55 – 53)/12 or (-55 + 53)/12
Ie. x = - 9 or -1/6.
Problems solved.
Hope that helped…like I said earlier though, just let me know if I haven’t made things clear.
happy sigh Thanks! That helped a bunch! Math is just so darn confusing! lol
You’re welcome! Glad I could help.