Question

What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?

Answer 1

Equation $2x^{2} + 42x + 260 = 6x$ is in form of $(x+9)^{2} = -49$ . All the intermediate steps are shown above for the transformation .

Step-by-step explanation:

We have the following equation 2x^2+42x+260=6x or $2x^{2} + 42x + 260 = 6x$ . Let's change this in form of (x+a)^2=b or $(x+a)^{2} = b$ , following steps will be all intermediate steps involved :

$2x^{2} + 42x + 260 = 6x$

⇒ $2x^{2} + 42x + 260 = 6x\\2(x^{2} + 21x+ 130) = 2(3x)\\(x^{2} + 21x+ 130) = 3x\\x^{2}+18x+130 = 0$

⇒$x^{2} + 18x+130 = 0\\x^{2}+ 2(9)x+ 81 + 49 = 0\\x^{2}+ 2(9)x+ 81 = -49$

But, $(x+9)^{2} = x^{2} + 18x+ 81$   Therefore,

⇒ $(x+9)^{2} = -49$

So , equation $2x^{2} + 42x + 260 = 6x$ is in form of $(x+9)^{2} = -49$ . All the intermediate steps are shown above for the transformation .