How do you solve -2t ( t + 2) = - 3?

2 Answers
Mar 18, 2018

t=(4+-sqrt40)/(-4)

Explanation:

-2t(t+2)=-3

Use the distributive property for the left side

(-2t)(t)+(-2t)(2)=-3

-2t^2 - 4t =-3

Then subtract color(red)(-3) on both sides

-2t^2 - 4t - color(red)(-3)=-3 - color(red)(-3)

-2t^2 - 4t + 3 = -3 + 3

-2t^2 - 4t + 3 = 0

Now we can use the quadratic formula with a=-2, b=-4, c=3

t= ((-b)+-sqrt(b^2-4ac))/(2a)

t=(-(-4)+-sqrt((-4)^2-4(-2)(3)))/((2)(-2))

t=(4+-sqrt(16+24))/(-4)

=>color(green)(t=(4+-sqrt(40))/(-4))

An equivalent simplified version:

t=(4+-2sqrt(10))/(-4)

t=-1+-(-1/2sqrt(10))

=>t=-1+-(-sqrt(5/2))

Mar 18, 2018

t~~-2.581
t~~0.581

Explanation:

You need to multiply the -2t with the parentheses and make the equation equal to 0.
-2t(t+2)=-3
-> -2t^2 -4t=-3
->-2t^2-4t+3=0

You now have a quadratic equation.

For the rest of this answer, I took a lot of this page (I encourage you to go take a look at it)

I will use the quadratic formula to solve it.

t=(-b+-sqrt(b^2-4ac))/(2a)

where at^2+bt+c=0

For -2t^2-4t+3=0 :

a=-2
b=-4
c=3

Now substitute into the quadratic formula:
t=(-(-4)+-sqrt((-4)^2-4(-2)(3)))/(2(-2))
t=(4+-sqrt(16+24))/(-4)
t=(4+-sqrt(40))/(-4)

Therefore:
t=(4+sqrt(40))/(-4)-> ~~-2.581
OR
t=(4-sqrt(40))/(-4)-> ~~0.581