Question

Complete the square to solve the equation below. X^2 + 2x - 14 = 10 A. x = 5; x = -4 B. x = -1; x = 4 C. x = -1; x = 3 D. x = -6; x = 4

Answer 1

Answer is D. X= -6, 4

Explanation:

Answer 2

Answer: The correct option is (D) x = -6, x = 4.

Step-by-step explanation: We are given to complete the square to solve the following quadratic equation :

`x^2+2x-14=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the following square formula :

`a^2+2ab+b^2=(a+b)^2.`

From equation (i), we have

`x^2+2x-14=10\\\\\Rightarrow x^2+2x=10+14\\\\\Rightarrow x^2+2* x*1+1^2=24+1^2\\\\\Rightarrow (x+1)^2=24+1\\\\\Rightarrow (x+1)^2=25\\\\\Rightarrow x+1=\pm√(25)~~~~~~~~~~~~~~~~~~~~~~~~~~~~`[\textup{taking square root on both sides}]\\\\\Rightarrow x+1=\pm5\\\\\Rightarrow x=-1\pm5\\\\\Rightarrow x=-1+5,~-1-5\\\\\Rightarrow x=4,~-6.`

Thus, the required solution of the given equation is x = -6 and x = 4.

Option (D) is CORRECT.