Mathematics: 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

1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4+1/4=2 2/4or: 1/4X9=2 2/4=2 1/2...

Complete the square to solve the equation below.

Ответ:

zahwaahmaf

17.01.2022

Mathematics

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

$x^2+2x-14=10\\\\\Rightarrow x^2+2x=10+14\\\\\Rightarrow x^2+2\times x\times1+1^2=24+1^2\\\\\Rightarrow (x+1)^2=24+1\\\\\Rightarrow (x+1)^2=25\\\\\Rightarrow x+1=\pm\sqrt{25}~~~~~~~~~~~~~~~~~~~~~~~~~~~~`[\textup{taking square root on both sides}]\\\\\Rightarrow x+1=\pm5\\\\\Rightarrow x=-1\pm5\\\\\Rightarrow x=-1+5,~-1-5\\\\\Rightarrow x=4,~-6.$

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

Option (D) is CORRECT.

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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

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