Question

Solve for x: 2(x + 3)2 − 4 = 0

Round your answer to the nearest hundredth.


A)x = 4.41, 1.59

B)x = 1.34, 5.24

C)x = −1.34, −5.24

D)x = −4.41, −1.59

Answer 1

Option D is correct

Explanation:

I took the test

Answer 2

Option D) x = −4.41, −1.59

Explanation:

We are given the following expression in the question:

`2(x + 3)^2 - 4 = 0`

Solving the above expression, we get:

`2(x + 3)^2 - 4 = 0\\2(x^2+9+6x)-4=0\\\text{Identity: }(a+b)^2 = a^2 + b^2 + 2ab\\2x^2+18+12x-4=0\\2x^2+12x+14=0\\\text{Using the quadratic formula:}\\ax^2 + bx +_ c = 0\\\\x = \displaystyle(-b\pm √(b^2-4ac))/(2a)\\\\\text{Puting a = 2, b = 12, c = 14}\\\\x = \displaystyle(-12\pm √((12)^2-4(2)(14)))/(2(2))\\\\x = (-12 \pm 5.65)/(4)\\\\x = (-12 + 5.65)/(4), (-12-5.65)/(4) = -1.5875, -4.4125 \approx -1.59, -4.14`