how to solve this equation with square root for 4x^2 + 6x -2 = -7

Question

i dont understand it

Answer 1

When in doubt you can always use the Quadratic Formula: X = (-b ±√(b²-4ac))/2a to solve or find the roots of any Quadratic Equation.
A quadratic equation is an equation that looks like: 0 = aX²+bX+c.

In your case with 4X²+6X-2 = -7 we just have to add seven to both sides to get:

4X²+6X+5 = 0.

This means a= 4, b = 6, c = 5

so we get,

X = (-6 ±√(6²-4(4)(5))/(2(4))

so 

X = (-6 ±√(36-80))/8
X = (-6 ±√(-44))/8

At this point if you have not learned about complex numbers you can just declare that there are no Real solutions.
This just means that the solutions to this equation falls outside of the realm of numbers that you currently know about. If you have learned about complex numbers read on.

The biggest perfect square that factors out of 44 is 4 leaving us a factor product of 4 and 11. So with that we know that √44=√(4)√(11) = 2√11

The 44 in this case is negative, hence we have to use i to denote the imaginary root, hence√-44=2√(11)i

Hence the final solutions are:

X = (-6 ± 2√(11)i)/8 = (3±√(11)i)/4 after dividing out a common 2.

Answer 2

Just follow step by step and understand.

4x² + 6x -2=0

4x² + 6x =2

2(2x² + 3x) =2

2x² + 3x =1

2(x² + (3/2)x) = 1

2((x+¾)² - (¾)²) = 1

2(x+¾)² - 2(¾)² = 1

2(x+¾)² = 1 + 2(¾)² = 1 + 18/16 = 34/16 = 17/8

(x+¾)² = 17/16

x+¾ = ±√(17)/4

x= -¾ ±√(17)/4 = (-3±√(17))/4