I'm sorry I wrote the problem wrong previously.
"The equation x^2-9x-1=0 has 2 solutions A and B. Where A < B.
x^2-9x-1=0
(x-9)x=1
x^2=9x+1
(x-9/2)^2-85/4=0
Solutions x=1/2(9- sq root 85)
and x=1/2(9 + sq root 85)
I also have a second similar problem. 2x^2+17x+2=0
x(2x +17)+2=0
16/273(x+17/4)^2=1
2(x+17/4)^2-273/8=0
Solutions x=1/4(-17- sq root 273)
or x=1/4(sq root 273-17)
Both these answers we marked wrong on my homework. Please help me
x^2-9x-1 = 0
x^2-9x = 1
x^2 - 9x + 81/4 = 1 + 81/4
(x - 9/2)^2 = 85/4
x - 9/2 = ±√85/2
x = 9/2 ±√85/2
= 1/2 (9±√85)
2x^2+17x+2 = 0
2x^2+17x = -2
2(x^2+17/2 x) = -1
x^2 + 17/2 + 289/16 = -1 + 289/16
(x + 17/4)^2 = 273/16
x + 17/4 = ±√273/4
x = -17/4 ±√273/4
= 1/4 (-17±√273)
To solve quadratic equations like the ones you provided, you can use the quadratic formula:
For an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Let's apply this formula to the first problem: x^2 - 9x - 1 = 0.
In this case, a = 1, b = -9, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-(-9) ± √((-9)^2 - 4(1)(-1))) / (2(1))
= (9 ± √(81 + 4)) / 2
= (9 ± √85) / 2
Now, it's important to note that A < B, which means the smaller solution is A and the larger solution is B.
Therefore, A = (9 - √85) / 2 and B = (9 + √85) / 2.
Now, let's move on to the second problem: 2x^2 + 17x + 2 = 0.
In this case, a = 2, b = 17, and c = 2.
Applying the quadratic formula:
x = (-(17) ± √((17)^2 - 4(2)(2))) / (2(2))
= (-17 ± √(289 - 16)) / 4
= (-17 ± √273) / 4
Again, A < B, so the smaller solution is A and the larger solution is B.
Hence, A = (−17 − √273) / 4 and B = (−17 + √273) / 4.
Make sure to carefully input these values in your homework to avoid any errors. If your answers match the solutions I provided, then they are correct.