solve for x?

Question

-2x^2=4x+1

Answer 1

-2x^2=4x+1
4x+1+2x^2=0
2x^2+4x+1=0
Using Quadratic formula: (-b(+/-) sqrt(b^2 -4ac))/2a
a=2
b=4
c=1

x= (-4 (+/-) sqrt(4^2 -4*2*1))/2*2
x= (-4 (+/-) sqrt(8))/4
x= (-4 (+/-) 2sqrt(2))/4
x= 1/2( -2 (+/-) sqrt(2))
either x= 1/2( -2 + sqrt(2)) or x= 1/2( -2 - sqrt(2))
either x= -0.293 or -1.708

Answer 2

-2x^2 = 4x + 1
0 = 2x^2 + 4x +1

delta = b^2 - 4ac ;so
delta = 4^2 - 4*2*1 = 16 - 8 = 8
the roots are in the formula

x = ( -b + sqrt[delta] ) / 2a and second x = ( -b - sqrt[delta] ) /2a

x = ( -4 + sqrt[ 8 ] ) / 2*2 = ( -4 + 2sqrt[ 2 ] ) / 4 ; the first
x = ( -4 - sqrt[ 8 ]) / 2*2 = ( -4 + 2sqrt[ 2 ] ) / 4 ; the second

Answer 3

First step is to make the equation = 0, so add 2x^2 to both sides.

2x^2 + 4x + 1 = 0

Now use the quadratic formula:

x = (-b (+/-) sqrt(b^2-4ac))/(2a)

x = (-4 + sqrt(4^2 - (4)(2)(1)))/((2)(1))
x = (-4 + sqrt(16-8))/2
x = (-4 + sqrt(8))/2
x = (-4 + 2sqrt(2))/2
x = -2 + sqrt(2)

also

x = -2 - sqrt(2)

Answer 4

The given equation is -2x^2=4x+1;

Re-writing the given equation, we get
2x^2+4x+1=0;

This equation is of the form ax^2+bx+c=0;

D=sqrt(b^2-4*a*c)
=sqrt(4^2-4*2*1)
=sqrt(16-8)=sqrt(8)//

The solution of a quadratic equation of the form ax^2+bx+c=0 is x=(-b+D)/2a and (-b-D)/2a

Therefore the 2 solutions for the given equation are:

x=(-4+2sqrt(2))/4 and (-4-2sqrt(2))/4

and x=(-1+sqrt(2)/2) & (-1-sqrt(2)/2)//

Answer 5

If you rewrite the equation to read -2x^2 - 4x - 1 = 0, you can then factor it. Factoring was never my strong suit when the coefficient isn't 1, so I can't help you there, but this should be enough to get you started.

Answer 6

rewriting the eqution:
-2x^2-4x-1=0
2x^2+4x+1=0
use x= -b(+-)sqrt(b^2-4ac)/2a
where b=4
a=2
c=1
just substitute & u get the ans

Answer 7

The first thing to notice is that there is only one variable: x. This makes things a little simpler.

The second thing to notice is that you don't have all the x-terms on one side. Generally it's a good idea to start by putting all the x-terms on the same side of the equation (I recommend moving the x^2 term to the right).

Then, note the type of equation, especially the number of the highest power (in this case, 2). Do you know any formula to solve it? What are the parameters that go into it?

Good luck!

Answer 8

-2x^2=4x+1

Combine terms,

2x² + 4x + 1 = 0

Using the quadratic equation
ax² + bx + c = 0
x = (b +- √(b² - 4ac))/2a

x = (-4 +- √(16 - 8))/2
x = (-4 +- √(8))/2

x = (-4 +- √(8))/2

x = (-2 + √(2), x = (-2 - √(2)

.
Q.E.D.

Answer 9

- 2x^2 = 4x + 1
2x^2 + 4x + 1 = 0
x = ( -4 +/- sqrt(16 - 8) ) / 4
= ( -4 +/- sqrt(8) ) / 4
= ( -4 +/- 2sqrt(2) ) / 4
= -1 +/- sqrt(2)/2
= -1 + sqrt(2)/2 or -1 - sqrt(2)/2.

Answer 10

-2x^2=4x+1
=>-2x^2-4x-1=0
=>2x^2+4x+1=0
Hence by quadratic formula
x={-4+-(sqrt)(16-8)}/4
=(-4+-sqrt8)/4
=(-4+-2.83)/4
=-1.17/4 or -6.83/4
= -0.293 or -1.708