Notice that the first and last terms are squares ( r 2 and 1). The trinomial r 2 + 2 r + 1 is a perfect square trinomial. (They are binomials, two terms, that are squared.) If you expand these, you get a perfect square trinomial. Some of the above examples have squared binomials: (1 + r) 2 and ( x – 2) 2 are squared binomials. However, you may be able to factor the expression into a squared binomial-and if not, you can still use squared binomials to help you.įirst, let’s look at squared binomials. Of course, quadratic equations often will not come in the format of the examples above. Applying the Square Root Property gives x – 3 =. Knowing the square root of 16 may have made you forget that to solve this equation, the squared quantity needs to be isolated Before taking the square root, add 2 to both sides: ( x – 3) 2 = 18. (Note that both the positive and negative square roots are included this is the other probable mistake.) So, x = 3 ±. There are two mistakes here: Knowing the square root of 16 may have made you forget that to solve this equation, the squared quantity needs to be isolated Before taking the square root, add 2 to both sides: ( x – 3) 2 = 18. Applying the Square Root Property gives x – 3 =, so x = 3 ±. Before taking the square root, add 2 to both sides: ( x – 3) 2 = 18. You forgot the negative square root when you took the square root of both sides. The -2.05 is an extraneous solution and must be discarded.Ĭorrect. Notice that a negative interest rate doesn’t make sense for this context, so only the positive value could be the interest rate. Simplifying the two equations gives two solutions to the equation. You now have two equations, one using 1.05 and one using −1.05. Subtract 1 from both sides to isolate r on the right. Using a calculator, you can find that is 1.05. Because (1 + r) 2 is a squared quantity you can use the Square Root Property. Only r is left, so try to isolate r.ĭividing both sides by 3000 leaves only (1 + r) 2 on the right. Substitute the values for the variables you know. The principal P is the original amount invested, so that is 3,000. The formula for compounding interest annually isĪ = P(1 + r) t, where A is the balance after t years, when P is the principal (initial amount invested) and r is the interest rate.įind the interest rate r if $3,000 is invested and grows to $3,307.50 after 2 years.įirst identify what you know.
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