Solve the quadratic equation 4x2+4x−3=04𝑥2+4𝑥−3=0 using the quadratic formula.(2 points)x = ,
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, the quadratic equation is: 4x^2 + 4x - 3 = 0
Therefore, a = 4, b = 4, and c = -3
Plugging these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4(4)(-3))) / 2(4)
x = (-4 ± √(16 + 48)) / 8
x = (-4 ± √64) / 8
x = (-4 ± 8) / 8
So, x = (4 + 8) / 8 or x = (4 - 8) / 8
This gives us two solutions for x:
x = 12 / 8 = 1.5
and
x = -4 / 8 = -0.5
Therefore, the solutions to the quadratic equation 4x^2 + 4x - 3 = 0 are x = 1.5 and x = -0.5.