 the quadratic formula. Consider the general equation ax squared plus bx plus c equals 0 remember that x is a variable whereas ab and c are parameters with a distinct from 0 and remember that all parameters are constants but not all constants are parameters how do we solve this quadratic equation for x? Let's complete the square we have this equation when we complete the square the first thing we do is we want the quadratic coefficient to be equal to 1 so let us divide by a we can do this because a is different from 0 so this is this becomes x squared plus b over a times x plus c over a equals 0 we may want to subtract this constant from both sides of the equation this is x squared plus bax equal to negative c over a now we know that to complete the square what we do is we divide the linear term by two and then square it so we divide the linear term by two and then we square it if we add it to one side we must add it to the other and these factors as x plus b over 2a squared now this can also be expressed as also now b squared over a squared and we take the square root both sides of this equation we get that x plus b over 2a is equal to plus or minus the square root of this expression if we we want to have the same denominator we multiply the first term by 4a then both the numerator and the denominator and we get 4 a c plus b squared we have that x is equal to minus b over 2a plus or minus the square root we can take the square root of the denominator and then rearrange these terms your b squared minus 4ax over the square root of 4a squared now we have that x is equal to minus b over 2a plus or minus the square root of b squared minus 4a times c over the square root of 4a squared which is just 2a now since we have the same denominator we have that x is equal to minus b plus or minus the square root of b squared minus 4ac over 2a which is the quadratic formula and now you can solve any quadratic equation