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 :

mkonsela62

Answer:

Answer is D. X= -6, 4

Step-by-step explanation:

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 :

[tex]x^2+2x-14=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following square formula :

[tex]a^2+2ab+b^2=(a+b)^2.[/tex]

From equation (i), we have

[tex]x^2+2x-14=10\\\\\Rightarrow x^2+2x=10+14\\\\\Rightarrow x^2+2\times x\times1+1^2=24+1^2\\\\\Rightarrow (x+1)^2=24+1\\\\\Rightarrow (x+1)^2=25\\\\\Rightarrow x+1=\pm\sqrt{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.[/tex]

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

Option (D) is CORRECT.

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