4t2-9t-35=0

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

1,t,1,1

Since 1,t,1,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1,1 then find LCM for the variable part t1.

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

Not prime

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

1

The factor for t1 is t itself.

t1=t

t occurs 1 time.

The LCM of t1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

t

t

Multiply each term in 4t2-9t-35=0 by t in order to remove all the denominators from the equation.

4t2⋅t-9t⋅t-35⋅t=0⋅t

Simplify each term.

Multiply t2 by t by adding the exponents.

Move t.

4(t⋅t2)-9t⋅t-35⋅t=0⋅t

Multiply t by t2.

Raise t to the power of 1.

4(t1t2)-9t⋅t-35⋅t=0⋅t

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

4t1+2-9t⋅t-35⋅t=0⋅t

4t1+2-9t⋅t-35⋅t=0⋅t

Add 1 and 2.

4t3-9t⋅t-35⋅t=0⋅t

4t3-9t⋅t-35⋅t=0⋅t

Cancel the common factor of t.

Move the leading negative in -9t into the numerator.

4t3+-9t⋅t-35⋅t=0⋅t

Cancel the common factor.

4t3+-9t⋅t-35⋅t=0⋅t

Rewrite the expression.

4t3-9-35⋅t=0⋅t

4t3-9-35t=0⋅t

4t3-9-35t=0⋅t

Multiply 0 by t.

4t3-9-35t=0

4t3-9-35t=0

Graph each side of the equation. The solution is the x-value of the point of intersection.

t≈-2.81994916,-0.25913148,3.07908064

Solve for t 4t^2-9/t-35=0