Solve for the roots in simplest form using the quadratic formula:
4, x, squared, plus, 69, equals, minus, 36, x
4x
2
+69=
−36x
To solve the equation using the quadratic formula, we need to set the equation in the form ax^2 + bx + c = 0, where a = 4, b = -36, and c = 69.
The quadratic formula is given as:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the given values, we have:
x = (-(-36) ± sqrt((-36)^2 - 4(4)(69))) / (2(4))
Simplifying further:
x = (36 ± sqrt(1296 - 1104)) / 8
x = (36 ± sqrt(192)) / 8
x = (36 ± 8√3) / 8
Dividing both the numerator and denominator by 4, we get:
x = (9 ± 2√3) / 2
So, the roots of the equation 4x^2 + 69 = -36x in simplest form are:
x = (9 + 2√3) / 2
x = (9 - 2√3) / 2