Solve for the roots in simplest form using the quadratic formula:
4, x, squared, plus, 20, x, equals, minus, 17
4x
2
+20x=
−17
To solve the equation using the quadratic formula, we need to first rewrite it in the form: ax^2 + bx + c = 0.
In this case, a = 4, b = 20, and c = -17.
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
x = (-20 ± √(20^2 - 4(4)(-17))) / (2(4))
Simplifying further:
x = (-20 ± √(400 + 272)) / 8
x = (-20 ± √(672)) / 8
x = (-20 ± 8√(21)) / 8
Finally, we can simplify by dividing both the numerator and denominator by 8:
x = (-20/8 ± 8√(21)/8)
x = (-5/2 ± √(21))