How are quadratic equations solved ? Please explain with the example: u^2 + 6u = 27.
We have to solve the equation u^2 + 6u = 27.
First bring all the terms to one side
=> u^2 + 6u - 27 = 0
One method of finding the roots which works when the roots are integers or fractions is to split the coefficient of u into two parts which add up to 6 and the product of which is -27. We can achieve this with 9 and -3.
=> u^2 + 9u - 3u - 27 = 0
remove the common factors of the first two terms and the last two terms.
=> u(u + 9) - 3(u + 9)
=>(u - 3)(u + 9) = 0
u - 3 = 0 => u = 3
and u + 9 = 0 => u = -9
This gives us the roots of the equation as 3 and -9.
Given the quadratic equation:
u^2 + 6u = 27
We need to solve for u.
First we will rewrite into the standard form.
==> u^2 + 6u - 27 = 0
Now we will factor the equation.
==> (u+9)(u-3) = 0
Now we will solve.
==> u1= -9 and u2= 3
Then, we have two solutions for the quadratic equations.
==> -9 and 3 are the roots for the equation.