Answer:
Converting the equation [tex]x^2-20x+13=0[/tex] into completing the square method we get: [tex]\mathbf{(x-10)^2=87}[/tex]
Step-by-step explanation:
we are given quadratic equation: [tex]x^2-20x+13=0[/tex]
And we need to convert it into completing the square method.
Completing the square method is of form: [tex]a^2-2ab+b^2=(a-b)^2[/tex]
Looking at the given equation [tex]x^2-20x+13=0[/tex]
We have a = x
then we have middle term 20x that can be written in form of 2ab So, we have a=x and b=? Multiplying 10 with 2 we get 20 so, we can say that b = 20
So, 20x in form of 2ab can be written as: 2(x)(10)
So, we need to add and subtract (10)^2 on both sides
[tex]x^2-20x+13=0\\x^2-2(x)(10)+(10)^2-(10)^2+13=0\\(x^2-2(x)(10)+(10)^2) \:can\: be\: written\: as\: (x-10)^2 \\(x-10)^2-100+13=0\\(x-10)^2-87=0\\(x-10)^2=87[/tex]
So, converting the equation [tex]x^2-20x+13=0[/tex] into completing the square method we get: [tex]\mathbf{(x-10)^2=87}[/tex]
