Question

-4x^2+(4/9)=0 -5x^2+(5/16)x=0

Answer 1

-4x**+ 4/9 = 0

-4x** = -4/9

x** = -4/9 * -1/4

x** =  1/9

x = 1/3

x = -1/3

 

-5x** + 5/16x = 0

5x(-x+ 1/16) = 0

5x = 0                           -x+1/16 = 0

x = 0                             -x = -1/16

                                     x = 1/16 

Answer 2

To solve these quadratic equations, we can use the quadratic formula:

For an equation of the form ax^2 + bx + c = 0, the quadratic formula states that the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Let's solve each equation step by step:

1. -4x^2 + (4/9) = 0:

Here, a = -4, b = 0, and c = 4/9.

Using the quadratic formula, we have:

x = (-0 ± √(0^2 - 4(-4)(4/9))) / (2(-4)) = (± √(0 - (-64/9))) / (-8) = (± √(64/9)) / (-8) = (± (8/3)) / (-8)

Simplifying further:

x = ± (8/3) / (-8) = ± (8/3) * (-1/8) = ± (1/3)

Therefore, the solutions for the first equation are x = 1/3 and x = -1/3.

2. -5x^2 + (5/16)x = 0:

Here, a = -5, b = 5/16, and c = 0.

Using the quadratic formula, we have:

x = (-(5/16) ± √((5/16)^2 - 4(-5)(0))) / (2(-5)) = (-(5/16) ± √(25/256)) / (-10) = (-(5/16) ± (5/16)) / (-10)

Simplifying further:

x = (-(5/16) + (5/16)) / (-10) or x = (-(5/16) - (5/16)) / (-10) = 0 / (-10) or x = (-10/16) / (-10) = 0 or x = 1/16

Therefore, the solutions for the second equation are x = 0 and x = 1/16.