Express x^2-5x+8 in the form (x-a)^2
Answers
Please mark me brain least Step-by-step explanation:
Given:
\begin{gathered}x^2 - 5x + 8 \\\\\end{gathered}
x
2
−5x+8
To Find:
\begin{gathered}\text{Put into the format : }(x - a)^2 + b \\\\\end{gathered}
Put into the format : (x−a)
2
+b
Method To Use:
\begin{gathered}\text{Completing the Square} \\\\\end{gathered}
Completing the Square
Solution:
\begin{gathered}\\\end{gathered}
\begin{gathered}x^2 - 5x + 8 \\\\\end{gathered}
x
2
−5x+8
Form a set of (b/2)² into the expression:
\begin{gathered}x^2 - 5x + (\dfrac{5}{2})^2 - (\dfrac{5}{2})^2 + 8 \\\\\end{gathered}
x
2
−5x+(
2
5
)
2
−(
2
5
)
2
+8
Rewrite (a² - 2ab + b²) as (a - b)² in the expression:
\begin{gathered}\bigg(x - \dfrac{5}{2}\bigg)^2 - (\dfrac{5}{2})^2 + 8 \\\\\end{gathered}
(x−
2
5
)
2
−(
2
5
)
2
+8
Combine the terms outside the (a - b)² in the expression:
\bigg(x - \dfrac{5}{2}\bigg)^2 - \dfrac{25}{4} + 8(x−
2
5
)
2
−
4
25
+8
\begin{gathered}\bigg(x - \dfrac{5}{2}\bigg)^2 + \dfrac{7}{4} \\\\\end{gathered}
(x−
2
5
)
2
+
4
7
Matching the expression with (x - a)² + b:
a = \dfrac{5}{2}a=
2
5
\begin{gathered}b = \dfrac{7}{4} \\\\\end{gathered}
b=
4
7