Solving the Equation(i don't know what to do)

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sw87

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I am having trouble solving (3x)^2=(3x+6)^2-(x+6)^2 I have tried many form of approching the problem and I feel I may be confusing myself more.
 
Did you try multiplying everything out, and collecting terms to one side?
 
yes but the subtraction sign is throughting me off. The answers I keep getting don't check back into the original problem.
 
I distributed the negative into the parentheses then does that make (-x-6)^2 equal (-x-6)(-x-6) or (-x-6)(-x+6)?
 
(3x)^2 I got 9x
(3x+6)^2 I got 9x+18x+18x+36
-(x+6)^2 i'm stuck
 
sw87 said:
(3x)^2 I got 9x Nope.

The parentheses show that each factor (both the 3 and the x) gets squared. You only squared the 3.

(3x+6)^2 I got 9x+18x+18x+36 Yup. But, again, x times x is x^2. So, 3x * 3x is 9x^2.

18x and 18x are like-terms, so combine them.

-(x+6)^2 i'm stuck Square x + 6, first. Then, multiply the result by -1.

That's the Order of Operations, right? "E"xponentiation before "M"ultiplication; in other words, E before M, in the acronym PEMDAS (a memory aid).

If you're confused by anything I write, please ask specific questions.
Click to expand...
 
(3x)^2=(3x+6)^2-(x+6)^2
9x^2=(3x+6)(3x+6)-(x+6)(x+6)
9x^2=9x^2+18x+18x+36-(x^2+6x+6x+36)
9x^2=9x^2+36x+36-x^2-12x-36
-9x^2 -9x^2
0=-x^2-9x^2+9x^2+36x-12x+36-36
0=-x^2+24x
+x^2 +x^2
x^2=24x
divide both sides by x
x=24
 
sw87 said:
(3x)^2=(3x+6)^2-(x+6)^2
9x^2=(3x+6)(3x+6)-(x+6)(x+6)
9x^2=9x^2+18x+18x+36-(x^2+6x+6x+36)
9x^2=9x^2+36x+36-x^2-12x-36
-9x^2 -9x^2
0=-x^2-9x^2+9x^2+36x-12x+36-36
0=-x^2+24x
+x^2 +x^2
x^2=24x
divide both sides by x We can't divide both sides by x because we don't know whether or not x is zero.

Sometimes it's okay to divide by x because there is given information of some sort that tells us the unknown variable is not zero. As long as we know that we are not dividing by something that could be zero, we're okay. That's not the case, in this exercise. We can't divide by x, here.
Click to expand...

x^2 - 24x = 0

The proper way to go is to factor the lefthand side, and then use something called the Zero-Product Property. (You used this property earlier, in your other thread, when you set each factor equal to zero.)
 
\(\displaystyle (3x)^2 = (3x + 6)^2 - (x + 6)^2\)

\(\displaystyle 9x^2 = 9x^2 + 36x + 36 - (x^2 + 12x + 36)\)

\(\displaystyle 0 = (36x - 12x) + (36 - 36) - x2\)

\(\displaystyle 0 = 24x - x^2\)

\(\displaystyle 0 = x(24 - x)\)
 
sw87 said:
0=x(24-x)
set both equal to 0
x=0 24-x=0
+x +x
x=24
x={0,24} This is correct.
Click to expand...

Check out my steps above, and see how combining like-terms as you go saves a little work.

You can also check your own solutions, by substituting (one at a time) 0 for x and 24 for x, in the original equation, and then do the arithmetic, to ensure that you end up with a true statement (like 0=0, or 5184=5184).
 
Thank You for all your help I have been stuck on this problem for 6 days. You helped me understand what I was don't wrong.
 
You said:
"I am having trouble solving (3x)^2 = (3x+6)^2 - (x+6)^2
...the subtraction sign is throughting me off."

You can get rid of the subtraction sign this way: (3x)^2 + (x+6)^2 = (3x+6)^2 ; kapish?

NOTE: in case your math teacher wants no English errors: throughting should be THROWING.
If you're not sure of the spelling of a word, LOOK IT UP: you won't regret it later...
 
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