4x2−12x+9=04{x}^{2}-12x+9=0
1
Rewrite 4x2−12x+94{x}^{2}-12x+9 in the form a2−2ab+b2{a}^{2}-2ab+{b}^{2}, where a=2xa=2x and b=3b=3.
(2x)2−2(2x)(3)+32=0{(2x)}^{2}-2(2x)(3)+{3}^{2}=0

2
Use Square of Difference: (a−b)2=a2−2ab+b2{(a-b)}^{2}={a}^{2}-2ab+{b}^{2}.
(2x−3)2=0{(2x-3)}^{2}=0

3
Take the square root of both sides.
2x−3=02x-3=0

4
Add 33 to both sides.
2x=32x=3

5
Divide both sides by 22.
x=32x=\frac{3}{2}

Done

Decimal Form: 1.5

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