Rewrite the equation by completing the square:
[tex](2x + 9)^2 = \frac{53}{4}[/tex]
Solution:
Given that,
[tex]2x^2 - 9x + 7 = 0[/tex]
We have to rewrite by completing the square
Step 1:
The general quadratic equation is given as:
[tex]ax^2 + bx + c = 0[/tex]
Compare with given, we get,
a = 2
b = -9
c = 7
Step 2:
From given,
[tex]2x^2 - 9x + 7 = 0[/tex]
Subtract 7 from both sides,
[tex]2x^2 - 9x = -7[/tex]
Step 3:
Find square of half of b
[tex](\frac{b}{2})^2 =( \frac{-9}{2})^2[/tex]
Add the term to each side of equation
[tex]2x^2 - 9x + (\frac{-9}{2})^2= -7 + (\frac{-9}{2})^2[/tex]
Simplify
[tex]2x^2 - 9x + (\frac{9}{2})^2= -7 + \frac{81}{4}\\\\2x^2 - 9x + (\frac{9}{2})^2= \frac{53}{4}[/tex]
The left side is of form:
[tex](a-b)^2 = a^2 - 2ab + b^2[/tex]
Therefore,
[tex](2x + 9)^2 = \frac{53}{4}[/tex]
Thus the solution is found
