Solve by factoring 2w^2-11=-12
I'm having a super hard time with factoring....can someone plz help?
plz help :<
see your later post, still with the typo.
To solve the equation 2w^2 - 11 = -12 by factoring, we'll rearrange the equation so that it is equal to zero:
2w^2 - 11 + 12 = 0
Combine like terms:
2w^2 + 1 = 0
Now, we want to factor this quadratic equation. Since the coefficient of w^2 is 2, we'll look for two binomials in the form of (aw + b)(cw + d) where a, b, c, and d are constants, and ac is equal to 2.
To factor 2w^2 + 1 = 0, we need to find two numbers that when multiplied give 2, and when added give 0 (since the coefficient of w is 0 in this case).
The factors of 2 are 1 and 2, but neither of them adds up to 0. Since no factors exist, this quadratic equation cannot be factored using integers.
In this case, we'll need to use the quadratic formula to find the solutions. The quadratic formula is:
w = (-b ± √(b^2 - 4ac)) / 2a
For 2w^2 + 1 = 0, a = 2, b = 0, and c = 1:
w = (-0 ± √(0^2 - 4 * 2 * 1)) / (2 * 2)
w = (± √(-8))/(4)
w = ±(√(8) * i) / 4
So, the solutions to the equation are:
w = (√(8) * i) / 4
w = - (√(8) * i) / 4
where i represents the imaginary unit.