Question

16a² - 2a +4 =-1
Solve equation by quadratic formula

Answer 1

a = (1 -i√79)/16 and a = (1 +i√79)/16

Explanation:

You want to solve the quadratic equation 16a² -2a +4 = -1 using the quadratic formula.

Standard form

The equation is written in standard form by adding 1 to both sides:

16a² -2a +5 = 0

The coefficients are (16, -2, 5) and are conventionally given the names (a, b, c). We will use those names in the quadratic formula, trusting you can avoid confusion with the variable name, which is also 'a'.

Formula

The solution to the equation ax² +bx +c = 0 is given by the formula ...

`x=(-b\pm√(b^2-4ac))/(2a)`

Using this formula, the solutions to the given quadratic are ...

`a=(-(-2)\pm√((-2)^2-4\cdot16\cdot5))/(2\cdot16)=(2\pm2√(-79))/(32)=(1\pm i√(79))/(16)`

The solutions to the equation are ...

a = (1 -i√79)/16 and a = (1 +i√79)/16