# Problem of the Week

## Updated at May 8, 2023 11:48 AM

This week we have another equation problem:

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

Let's start!

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

 1 Move all terms to one side.$w+4{w}^{2}-5=0$2 Split the second term in $$w+4{w}^{2}-5$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times -5=-20$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-20$$?$$5$$ and $$-4$$3 Split $$w$$ as the sum of $$5w$$ and $$-4w$$.$4{w}^{2}+5w-4w-5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4{w}^{2}+5w-4w-5=0$3 Factor out common terms in the first two terms, then in the last two terms.$w(4w+5)-(4w+5)=0$4 Factor out the common term $$4w+5$$.$(4w+5)(w-1)=0$5 Solve for $$w$$.1 Ask: When will $$(4w+5)(w-1)$$ equal zero?When $$4w+5=0$$ or $$w-1=0$$2 Solve each of the 2 equations above.$w=-\frac{5}{4},1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=-\frac{5}{4},1$DoneDecimal Form: -1.25, 1w=-5/4,1