Algebra for police test - solve for x

hmac

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3(x+2)^2-25 = 50

^ (is the symbol for to the power of)

Can someone walk me through this?

The answer is 3.

I need to know how to get that.
 
3(x+2)^2-25 = 50

^ (is the symbol for to the power of)

Can someone walk me through this?

The answer is 3.

I need to know how to get that.

I like to simplify equations whenever possible. Remember when you do the same to both sides of the equation, it does not change the value of the equation.
I will walk you through this one as I would do it.
Step 1; add 25 to both sides of the equation.
3 (x+2)^2 -25+25 = 50 +25
3 (x+2)^2 = 75
Step 2 divide both sides by 3
(x+2)^2 =25
Step 3: take the square root of both sides.

x +2 = 5;
Step 4; subtract 2 from both sides.
X-2-2 = 5-2
X = 3

I hope this helps you.
Mstutor
 
I like to simplify equations whenever possible. Remember when you do the same to both sides of the equation, it does not change the value of the equation.
I will walk you through this one as I would do it.
Step 1; add 25 to both sides of the equation.
3 (x+2)^2 -25+25 = 50 +25
3 (x+2)^2 = 75
Step 2 divide both sides by 3
(x+2)^2 =25
Very nice! Well done.

Step 3: take the square root of both sides.

x +2 = 5;
One comment here: there are two number whose square is "a", \(\displaystyle \sqrt{a}\) and \(\displaystyle -\sqrt{a}\)
Here \(\displaystyle (x+ 2)^2= 25\) means that x+ 2= 5 or x+ 2= -5.

Step 4; subtract 2 from both sides.
X-2-2 = 5-2
X = 3

I hope this helps you.
Mstutor
But \(\displaystyle x+ 2= -5\) gives \(\displaystyle x= -7\) also satisfies the equation.
The 'answer' is NOT just 3. The two solutions are 3 and -7.
 
3(x+2)^2-25 = 50

^ (is the symbol for to the power of)

Can someone walk me through this?

The answer is 3.

I need to know how to get that.

(1) Use FOIL method.

(x+2)^2 = x^2+4x+4

We now have 3(x^2+4x+4) - 25 = 50.

(2) Distribute 3 to remove parentheses.

3(x^2+4x+4) = 3x^2+12x+12.

We have 3x^2+12x+12 - 25 = 50.

3x^2+12x-13 = 50.

(3) Subtracting 50 from both sides we get 3x^2+12x-63 = 0

(4) Divide across by 3

x^2+4x-21 = 0

(5) Factor

(x-3)(x+7) = 0

(6) Set each factor = 0 and solve for x


X-3=0

X = 3

X+7 = 0

X = -7

After plugging x = -7 and x= 3, I found that both answers satisfy the original equation given.

Thus, the answer is x = -7 and x = 3.
 
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