Answer:
<h2>4/25</h2>
Step-by-step explanation:
Given the incomplete quadratic equation
, we are to complete it so that the result will be the square of a binomial. To do that, we will use the completing the square method.
Completing the square method is a way of completing a quadratic equation by solving for a constant to add that will make the quadratic equation a perfect square of a binomial.
To get the constant term using the method, we will take the square of the alf of the coefficient of x in the equation given.
Coefficient of x = 4/5
half of the coefficient of x = 1/2(4/5)
half of the coefficient of x = 4/10 = 2/5
Square of the half of the coefficient of x = (2/5)²
Square of the half of the coefficient of x = 4/25
Hence the constant that we will use to complete the equation to make if a square of a binomial is 4/25
The equation will become:
![= \[x^2 + \dfrac{4}{5}x +\dfrac{4}{25} \\\\= \[x^2 + \dfrac{4}{5}x +(\dfrac{2}{5})^2\\\\= (x +\dfrac{2}{5})^2](https://tex.z-dn.net/?f=%3D%20%5C%5Bx%5E2%20%2B%20%5Cdfrac%7B4%7D%7B5%7Dx%20%2B%5Cdfrac%7B4%7D%7B25%7D%20%5C%5C%5C%5C%3D%20%20%5C%5Bx%5E2%20%2B%20%5Cdfrac%7B4%7D%7B5%7Dx%20%2B%28%5Cdfrac%7B2%7D%7B5%7D%29%5E2%5C%5C%5C%5C%3D%20%20%28x%20%2B%5Cdfrac%7B2%7D%7B5%7D%29%5E2)
<em>Hence the constant value that will make the resulting quadratic the square of a binomial is 4/25</em>