find a value for k that will make 4x^2 + 6.4x + k a perfect square. describe the procedure that you used which requires algebra. I have the answer and it is k = 1.6^2 or 2.56 i just don't get how we got there
I gave you the answer yesterday. I picked 2.56 because
4x^2 + 6.4x + 2.56 = (2x + 1.6)^2
is a "perfect square", as you can verify by multiplication.
1.6 is the number which, when multiplied by twice the square root of 4 (the first coefficient) gives the second coefficient, 6.4.
To find a value for k that will make the quadratic expression 4x^2 + 6.4x + k a perfect square, you can follow a few algebraic steps. The idea is to rewrite the given quadratic expression as a perfect square trinomial.
1. Start with the quadratic expression: 4x^2 + 6.4x + k.
2. Notice that the quadratic term, 4x^2, is a perfect square: (2x)^2 = 4x^2.
3. Now, focus on the linear term, 6.4x. We need to figure out what expression, when squared, gives us this term.
6.4x can be rewritten as 2 * sqrt(k) * 2x. To see this, observe that 6.4x = 2 * sqrt(k) * 2x.
From this, we can conclude that sqrt(k) = sqrt(1.6), since 6.4 / 4 = 1.6.
Therefore, k = (sqrt(1.6))^2.
4. Simplifying further, we have k = 1.6^2 = 2.56.
So, to make 4x^2 + 6.4x + k a perfect square, we need the value of k to be 2.56.
By following these steps, you can determine the value of k that makes the quadratic expression a perfect square.