How do you factor and solve #2x^2+2x-2=0#?

Question

Eli Assouline · Accepted Answer

this equation cannot be solved by factorization that means it takes a lot of effort and time and hence we have to use the quadratic formula.

given equation #x^2+x-1=0# first we have to check the nature of the roots by using discriminant #D=b^2-4ac# substituting the values of #b=1,a=1,c=-1# we get #D=1+4=5>0# hence we have real and distinct roots applying the quadratic formula#color(red)[(-b+-sqrt(b^2-4ac))/(2a)]rArr[(-1+-sqrt(1+4))/2]rArr(-1+-sqrt5)/2# hence the roots are #(-1+-sqrt5)/2#

Ethan Adkins · Answer

undefined To factor and solve the quadratic equation $2x^2 + 2x - 2 = 0$, you can first factor out the greatest common factor, which is 2. Then, you can use the quadratic formula $(-b \pm \sqrt{b^2 - 4ac}) / (2a)$ to find the solutions.

After factoring out the greatest common factor, the equation becomes $2(x^2 + x - 1) = 0$.

Then, apply the quadratic formula:
$a = 1$, $b = 1$, and $c = -1$.

Using the quadratic formula, the solutions are:
$x = \frac{{-1 + \sqrt{1^2 - 4 \cdot 1 \cdot (-1)}}}{2 \cdot 1}$ and $x = \frac{{-1 - \sqrt{1^2 - 4 \cdot 1 \cdot (-1)}}}{2 \cdot 1}$.

Solving these equations yields:
$x = \frac{{-1 + \sqrt{5}}}{2}$ and $x = \frac{{-1 - \sqrt{5}}}{2}$.