-q200+2q200=722q

Factor 2 out of 2q.

-q200+2(q)200=722q

Factor 2 out of 200.

-q200+2q2⋅100=722q

Cancel the common factor.

-q200+2q2⋅100=722q

Rewrite the expression.

-q200+q100=722q

-q200+q100=722q

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

200,100,q

Since 200,100,q contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 200,100,1 then find LCM for the variable part q1.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The prime factors for 200 are 2⋅2⋅2⋅5⋅5.

200 has factors of 2 and 100.

2⋅100

100 has factors of 2 and 50.

2⋅2⋅50

50 has factors of 2 and 25.

2⋅2⋅2⋅25

25 has factors of 5 and 5.

2⋅2⋅2⋅5⋅5

2⋅2⋅2⋅5⋅5

The prime factors for 100 are 2⋅2⋅5⋅5.

100 has factors of 2 and 50.

2⋅50

50 has factors of 2 and 25.

2⋅2⋅25

25 has factors of 5 and 5.

2⋅2⋅5⋅5

2⋅2⋅5⋅5

The number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 200,100,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅2⋅5⋅5

The LCM of 200,100,1 is 2⋅2⋅2⋅5⋅5=200.

Multiply 2 by 2.

4⋅2⋅5⋅5

Multiply 4 by 2.

8⋅5⋅5

Multiply 8 by 5.

40⋅5

Multiply 40 by 5.

200

200

The factor for q1 is q itself.

q1=q

q occurs 1 time.

The LCM of q1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

q

The LCM for 200,100,q is the numeric part 200 multiplied by the variable part.

200q

200q

Multiply each term in -q200+q100=722q by 200q in order to remove all the denominators from the equation.

-q200⋅(200q)+q100⋅(200q)=722q⋅(200q)

Simplify -q200⋅(200q)+q100⋅(200q).

Simplify each term.

Cancel the common factor of 200.

Move the leading negative in -q200 into the numerator.

-q200⋅(200q)+q100⋅(200q)=722q⋅(200q)

Factor 200 out of 200q.

-q200⋅(200(q))+q100⋅(200q)=722q⋅(200q)

Cancel the common factor.

-q200⋅(200q)+q100⋅(200q)=722q⋅(200q)

Rewrite the expression.

-q⋅q+q100⋅(200q)=722q⋅(200q)

-q⋅q+q100⋅(200q)=722q⋅(200q)

Raise q to the power of 1.

-(q1q)+q100⋅(200q)=722q⋅(200q)

Raise q to the power of 1.

-(q1q1)+q100⋅(200q)=722q⋅(200q)

Use the power rule aman=am+n to combine exponents.

-q1+1+q100⋅(200q)=722q⋅(200q)

Add 1 and 1.

-q2+q100⋅(200q)=722q⋅(200q)

Rewrite using the commutative property of multiplication.

-q2+200q100q=722q⋅(200q)

Cancel the common factor of 100.

Factor 100 out of 200.

-q2+100(2)q100q=722q⋅(200q)

Cancel the common factor.

-q2+100⋅2q100q=722q⋅(200q)

Rewrite the expression.

-q2+2q⋅q=722q⋅(200q)

-q2+2q⋅q=722q⋅(200q)

Multiply q by q by adding the exponents.

Move q.

-q2+2(q⋅q)=722q⋅(200q)

Multiply q by q.

-q2+2q2=722q⋅(200q)

-q2+2q2=722q⋅(200q)

-q2+2q2=722q⋅(200q)

Add -q2 and 2q2.

q2=722q⋅(200q)

q2=722q⋅(200q)

Simplify 722q⋅(200q).

Rewrite using the commutative property of multiplication.

q2=200722qq

Multiply 200722q.

Combine 200 and 722q.

q2=200⋅722qq

Multiply 200 by 722.

q2=144400qq

q2=144400qq

Cancel the common factor of q.

Cancel the common factor.

q2=144400qq

Rewrite the expression.

q2=144400

q2=144400

q2=144400

q2=144400

Take the square root of both sides of the equation to eliminate the exponent on the left side.

q=±144400

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite 144400 as 3802.

q=±3802

Pull terms out from under the radical, assuming positive real numbers.

q=±380

q=±380

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

q=380

Next, use the negative value of the ± to find the second solution.

q=-380

The complete solution is the result of both the positive and negative portions of the solution.

q=380,-380

q=380,-380

q=380,-380

q=380,-380

Solve for q -q/200+(2q)/200=722/q