Problem of the Week

Updated at Dec 21, 2020 2:08 PM

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Mar 24, 2025

This week we have another equation problem:

How would you solve $t(4t-3)=27$ ?

Let's start!

t(4t-3)=27

Expand.

4{t}^{2}-3t=27

Move all terms to one side.

4{t}^{2}-3t-27=0

Split the second term in

4{t}^{2}-3t-27

into two terms.

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

4\times -27=-108

Ask: Which two numbers add up to

-3

and multiply to

-108

9

and

-12

Split

-3t

as the sum of

9t

and

-12t

4{t}^{2}+9t-12t-27

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4{t}^{2}+9t-12t-27=0

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

t(4t+9)-3(4t+9)=0

Factor out the common term

4t+9

(4t+9)(t-3)=0

Solve for

t

Ask: When will

(4t+9)(t-3)

equal zero?

When

4t+9=0

t-3=0

Solve each of the 2 equations above.

t=-\frac{9}{4},3

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t=-\frac{9}{4},3

Done

Decimal Form: -2.25, 3