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# Quadratic Formula

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Equation / Last modified by Administrator on 2015/12/24 07:08
`"Quadratic Solutions" = `

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vCalc.Quadratic Formula

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This is the equation for the solution of a second order polynomial of the form `aX^2+bX+C = 0` where the solution produces two roots

`(-b +- sqrt(b^2 -4ac))/(2a)`

# Notes

Solving the quadratic equation.

Suppose **`a x^2+b x+c=0`** and `a!=0`

first divide by `a` to get:

`x^2+b/a x+c/a=0`

Then complete the square and obtain:

`x^2+b/a x+(b/(2a))^2-(b/(2a))^2+c/a=0`

The first three terms factor:

`(x+b/(2a))^2=(b^2)/(4a^2)-c/a`

Take square roots on both sides to get

`x+b/(2a)=+-sqrt((b^2)/(4a^2)-c/a)`

Finally move the b/(2a) to the right and simplify to get the two solutions:

** `x_(1,2)=(-b+-sqrt(b^2-4a c))/(2a)`**

This equation,

**Quadratic Formula**, is used in 1 calculator.**Calculators**