Question

Which shows the equation below written in standard form? 13 - 6x = (2x - 5)2 + 3
a. 4x2 - 14x - 15 = 0
b. 4x2 - 14x + 15 = 0
c. 4x2 - 26x + 15 = 0
d. 4x2 - 26x - 15 = 0

Answer 1

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 2

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.