Problem of the Week

Updated at Sep 26, 2022 11:58 AM

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Mar 24, 2025

This week we have another equation problem:

How would you solve the equation $y(4y+2)=72$ ?

Let's start!

y(4y+2)=72

Expand.

4{y}^{2}+2y=72

Move all terms to one side.

4{y}^{2}+2y-72=0

Factor out the common term

2

2(2{y}^{2}+y-36)=0

Split the second term in

2{y}^{2}+y-36

into two terms.

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

2\times -36=-72

Ask: Which two numbers add up to

1

and multiply to

-72

9

and

-8

Split

y

as the sum of

9y

and

-8y

2{y}^{2}+9y-8y-36

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2(2{y}^{2}+9y-8y-36)=0

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

2(y(2y+9)-4(2y+9))=0

Factor out the common term

2y+9

2(2y+9)(y-4)=0

Solve for

y

Ask: When will

(2y+9)(y-4)

equal zero?

When

2y+9=0

y-4=0

Solve each of the 2 equations above.

y=-\frac{9}{2},4

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y=-\frac{9}{2},4

Done

Decimal Form: -4.5, 4