Problem of the Week

Updated at May 13, 2024 9:34 AM

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Mar 24, 2025

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation $7+4u+\frac{5}{u}=16$ ?

Check out the solution below!

7+4u+\frac{5}{u}=16

Multiply both sides by

u

7u+4{u}^{2}+5=16u

Move all terms to one side.

7u+4{u}^{2}+5-16u=0

Simplify

7u+4{u}^{2}+5-16u

-9u+4{u}^{2}+5

-9u+4{u}^{2}+5=0

Split the second term in

-9u+4{u}^{2}+5

into two terms.

Multiply the coefficient of the first term by the constant term.

4\times 5=20

Ask: Which two numbers add up to

-9

and multiply to

20

-4

and

-5

Split

-9u

as the sum of

-4u

and

-5u

4{u}^{2}-4u-5u+5

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4{u}^{2}-4u-5u+5=0

Factor out common terms in the first two terms, then in the last two terms.

4u(u-1)-5(u-1)=0

Factor out the common term

u-1

(u-1)(4u-5)=0

Solve for

u

Ask: When will

(u-1)(4u-5)

equal zero?

When

u-1=0

4u-5=0

Solve each of the 2 equations above.

u=1,\frac{5}{4}

To get access to all 'How?' and 'Why?' steps, join Cymath Plus!

u=1,\frac{5}{4}

Done

Decimal Form: 1, 1.25