Use the quadratic formula to solve. Express your answer in simplest form. 10t^2+21t+6=2t

Answer 1

Hi Gabriella,

10t² +21t + 6 = 2t

First subtract 2t from both sides so that you have it in the form ax² + bx + c = 0 (at² + bt + c = 0 in this case)

Then you can use the quadratic formula. If you proceed correctly you should be able to find a positive perfect square number under the radical part of the equation. The plus and minus feature of the formula should allow you to find two answers, both fractions.

As a hint, the answers you seek are the same as for this equation: (5x + 2)(2x + 3) = 0

If those hints aren't enough, return here with narrower questions.

Enjoy

Answer 2

First we have to make sure we're setup for the quadratic formula with an equation like: ax² + bx + c = 0.

10t² + 21t + 6 = 2t

Subtract 2t from both sides and we're there.

10t² + 19t + 6 = 0

Now we'll use the quadratic formula, and we know that a = 10, b = 19, and c = 6.

t = (-b ± √(b² - 4ac)) / 2a

t = (-19 ± √(19² - 4(10)(6))) / 2(10)

t = (-19 ± √(361 - 240)) / 20

t = (-19 ± √121) / 20

t = (-19 ± 11) / 20

t = (-19 + 11) / 20 or (-19 - 11) / 20

t = -8/20 or -30/20

t = -2/5 or -3/2