# Problem of the Week

Updated at Jan 7, 2019 2:41 PM

For this week we've brought you this equation problem.

How would you solve $$4t-5-\frac{5}{t}=\frac{1}{2}$$?

Here are the steps:

$4t-5-\frac{5}{t}=\frac{1}{2}$

 1 Multiply both sides by $$2t$$$8{t}^{2}-10t-10=t$2 Move all terms to one side$8{t}^{2}-10t-10-t=0$3 Simplify $$8{t}^{2}-10t-10-t$$ to $$8{t}^{2}-11t-10$$$8{t}^{2}-11t-10=0$4 Split the second term in $$8{t}^{2}-11t-10$$ into two termsHow?1 Multiply the coefficient of the first term by the constant term$8\times -10=-80$2 Ask: Which two numbers add up to $$-11$$ and multiply to $$-80$$?$$5$$ and $$-16$$3 Split $$-11t$$ as the sum of $$5t$$ and $$-16t$$$8{t}^{2}+5t-16t-10$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$8{t}^{2}+5t-16t-10=0$5 Factor out common terms in the first two terms, then in the last two terms$t(8t+5)-2(8t+5)=0$6 Factor out the common term $$8t+5$$$(8t+5)(t-2)=0$7 Solve for $$t$$How?1 Ask: When will $$(8t+5)(t-2)$$ equal zero?When $$8t+5=0$$ or $$t-2=0$$2 Solve each of the 2 equations above$t=-\frac{5}{8},2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$t=-\frac{5}{8},2$DoneDecimal Form: -0.625, 2t=-5/8,2