Problem of the Week

Updated at May 8, 2023 11:48 AM

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Mar 24, 2025

This week we have another equation problem:

How can we solve the equation $w+4{w}^{2}=5$ ?

Let's start!

w+4{w}^{2}=5

Move all terms to one side.

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

Split the second term in

w+4{w}^{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

1

and multiply to

-20

5

and

-4

Split

w

as the sum of

5w

and

-4w

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

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

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

w(4w+5)-(4w+5)=0

Factor out the common term

4w+5

(4w+5)(w-1)=0

Solve for

w

Ask: When will

(4w+5)(w-1)

equal zero?

When

4w+5=0

w-1=0

Solve each of the 2 equations above.

w=-\frac{5}{4},1

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w=-\frac{5}{4},1

Done

Decimal Form: -1.25, 1