Help please?

Question

What is the solution to 2x^2+4x=-3? Showing me how to get to the solution will be very helpful. Thank you in advance

Answer 1

2x^2+4x=-3

2x^2+4x+3 = 0

Use quadratic formula:
x = [-b +/- √(b^2 - 4ac)] / 2a

x = [-4 +/- √(16 - 4(2)(3))] / 2(2)

x = [-4 +/- √(16-24)] / 4
x = [-4 +/- √(-8)] / 4
x = [-4 +/- √(-1*4*2)] / 4
x = [-4 +/- 2i√(2)] / 4

2 answers:
x = [-4 + 2i√(2)] / 4
and
x = [-4 - 2i√(2)] / 4

PS if you would like, you can reduce this answer further:

x = -4/4 + [2i√(2)] / 4
x = -1 + [i√(2)] / 2
and
x = -4/4 - [2i√(2)] / 4
x = -1 - [i√(2)] / 2

Answer 2

A slight rearrangement will put the thing into standard form: 2x*2 + 4x + 3 = 0. This can be solved using the standard quadratic formula to get x = -4 +/- sqrt(16 - 24) = 4 +/- 2 sqrt(2) i.

Answer 3

2x^2+4x=-3

2x² + 4x + 3 = 0

Solve using quadratic formula

ax² + bx + c = 0
x = (-b ± √(b² - 4ac))/2a

x = (-4 ± √(16 - 24))/4

x = (-4 ± √(-8))/4

x = (-4 ± 2i√2)/4

x = -1 ± 0.5i√2
.

Answer 4

move negative three to other side:
2x^2 + 4x + 3 = 0

factor:
(2x + 3) (x + 1) = 0

set each equal to zero:
2x + 3 = 0
and
x + 1 = 0

solve for zero:
2x = -3
x = -3/2
and
x = -1

Answer 5

you can do this

2x^2+4x+3=0
this is a quadratic expression. So you can factor

Answer 6

2x^2 + 4x = -3
2x^2 + 4x + 3 = 0 : standard form
(2x + 1)* (x +3) = 0 : factor
2x + 1 = 0
x = -0.5 1st answer
x + 3 = 0
x = -3: 2nd answer