Give me an equation, and I will solve it

[Alolan_Apples]

This thread is kinda similar to these "ask me" threads, but I'm interested into solving algebraic equations and trigonometric equations. If you have an equation to share, you can post it here, and I can solve it by showing some steps. However, I'm not gonna do your homework. I'm just wanting to solve some equations for fun. But I can't graph them. That would require using attachments, and I primarily use the iPhone and iPad to browse this site.

So what algebraic equations do you have?

 

[toadsworthy]

(x-1)^2 = (4 * (square root(x-4))^2

sorry I can't put the superscript or square root symbol so I hope you can understand it

 

[Alolan_Apples]

(x-1)^2 = (4 * √(x-4))^2

x=13, x=5

Spoiler: Steps

(x-1)^2 = (4 * √(x-4))^2
x-1 = 4√(x-4)
(x-1)/4=√(x-4)
(x-1)^2/16=x-4
(x-1)^2=16x-64
x^2-2x+1=16x-64
x^2-18x+65=0
(x-13)(x-5)=0
x-13=0 or x-5=0
x=13 or x=5

((13)-1)^2=(4 * √(13-4))^2
12^2=(4*√9)^2
12^2=(4*3)^2
144=144
GOOD

((5)-1)^2=(4 * √(5-4))^2
4^2=(4*√1)^2
16=16
GOOD

 

[SensaiGallade]

I hope you can do calculus!

y=f(x)

f(x)=2x^3 + 4x^2 + 5x + 8

Find f'(x) and f''(x).

 

[Alolan_Apples]

y=2x^3 + 4x^2 + 5x + 8

y'=6x^2+8x+5

y''=12x+8

Spoiler: Steps

y=2x^3+4x^2+5x+8
d/dx(2x^3)+d/dx(4x^2)+d/dx(5x)+d/dx(8)
d/dx(2x^3) = 3*2x^(3-1) = 6x^2
d/dx(4x^2) = 2*4x^(2-1) = 8x
d/dx(5x) = 1*5x^(1-1) = 5
d/dx(8) = 0
y'=6x^2+8x+5

y'=6x^2+8x+5
d/dx(6x^2)+d/dx(8x)+d/dx(5)
d/dx(6x^2) = 2*6x^(2-1) = 12x
d/dx(8x) = 1*8x^(1-1) = 8
d/dx(5) = 0
y''=12x+8

I could do the basic differentiation rules (which includes the product rule and chain rule) and the basic integration rules (which includes initial value problems and reverse chain rule substitution) very well, but just giving you a heads up, I'm planning on taking Calculus this fall (or at least another time), and when I took it in high school, I didn't do very well. For this reason, I couldn't do word problems or some of the more advanced stuff. But I will accept basic differentiation problems and basic integration problems, as well as proving trig identities.

 

[Alolan_Apples]

1/B=U*√(M^2)*ln(e^P)
1/B=U*M*ln(e^P)
1/B=U*M*P
1=BUMP

This is how I'll bump this thread if it gets inactive. Anymore equations for me?

 

[xSuperMario64x]

Screw math. Especially calculus.

But seriously, here's a good, easy one... this is from my pre-calculus class.

Find the amount A accumulated after investing a principal $3950 for 8 years at an interest rate 8.1% compounded continuously.
Use the equation A=Pe^rt to solve it.

 

[Xerolin]

my brain doesn't want this for the future years