Question

Complete the square to solve the equation below x^2+10x+10=14

Answer 1

Option A is the correct option.

Explanation:

The given equation is x²+10x+10 = 14

we further solve this equation

x² + 10x + 10 - 14 = 14 - 14

x² + 10x - 4 = 0

Now we can get the solutions of the given equation by quadratic formula.

Value of x in ax²+bx+c = 0 is

`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`

`x=(-10\pm √(100-4* 1* (-4)))/(2)`

`=(-10\pm √(100+16))/(2)`

`=(-10\pm 2√(29))/(2)`

`=-5\pm √(29)`

x = -5 + √29 , x = -5 - √29

Therefore option A is the answer.

Answer 2

Option A is correct, i.e. x = -5+√29, and x = -5-√29.

Explanation:

Given the equation is x^2 +10x +10 = 14.

Rewriting the equation in form of perfect square like x^2 + 2ax + a^2,

x^2 + 2(5)x + 10 + 15 = 14 + 15.

x^2 + 2(5)x + 25 = 29.

We know the formula:- x^2 + 2ax + a^2 = (x+a)^2.

x^2 + 2(5)x + 5^2 = 29.

(x+5)^2 = 29.

x+5 = ±√29.

x = -5 ±√29.

Hence, option A is correct, i.e. x = -5+√29, and x = -5-√29.