Answered

Which shows the equation below written in standard form? 13 - 6x = (2x - 5)2 + 3

A4x2 - 14x - 15 = 0
B4x2 - 14x + 15 = 0
C4x2 - 26x + 15 = 0
D4x2 - 26x - 15 = 0

Verified Answer :

Billymkhoi

13 -6x= (2x-5)^2+ 3
⇒ 13 -6x= 4x^2 -20x+ 25+ 3
⇒ 4x^2 -20x+ (25+3)= 13 -6x 
⇒ 4x^2 -20x +6x+ 28 -13= 0
⇒ 4x^2+ (-20x+ 6x)+ (28-13)= 0 (combine like terms)
⇒ 4x^2 -14x+ 15= 0

The correct answer is b. 4x^2 -14x+ 15= 0~

Answer: The correct option is (b) \(4x^2-14x+15=0.\)

Step-by-step explanation:  The given equation is

\(13-6x=(2x-5)^2+3.~~~~~~~~~~~~~(i)\)

We are given to select the correct standard form of the above equation.

We will be using the following formula:

\((a-b)^2=a^2-2ab+b^2.\)

From equation (i), we have

\(13-6x=(2x-5)^2+3\\\\\Rightarrow 13-6x=4x^2-20x+25+3\\\\\Rightarrow 13-6x=4x^2-20x+28\\\\\Rightarrow 4x^2-20x+28-13+6x=0\\\\\Rightarrow 4x^2-14x+15=0.\)

Therefore, the correct standard form is \(4x^2-14x+15=0.\)

Thus, (b) is the correct option.

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