In the quadratic equation x2 - 8x + a = 0; what is the value, a, in order to form a perfect square?
Mathematics · Middle School · Tue Nov 03 2020
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Given the quadratic equation:
x^2 - 8x + a = 0
Find the value of a in order to make the quadratic equation a perfect square.
Solution:
In order to make the quadratic equation a perfect square, we take a look at it's original formula.
x^2 + 2xy + y^2
Noticed that 2 is multiplied in the second term, with the value 2xy, and since x is already 1, in order to find y, we need to find the current value by 2, and square the answer.
Since we are given -8 in the middle, dividing it by 2 will give an answer of -4. Now that we know that the missing number is -4, we simply square it in order to make it a perfect square.
=-4^2
= 16
The final equation will be:
x^2 - 8x + 16
The factored form will be:
(x - 4)^2