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Theory:

Quadratic equation
A quadratic equation in the variable \(x\) is an equation of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\) and \(c\) are numbers, \(a \ne 0\). The degree of the quadratic equation is \(2\).
Important!
The equation \(ax^2 + bx + c = 0\) is called the standard form of a quadratic equation.
Roots of a quadratic equation
The value of \(x\) that makes the expression \(ax^2 + bx + c\) is zero, called the roots of the quadratic equation.
Consider the quadratic equation \(ax^2 + bx + c = 0\), where \(a \ne 0\)
 
Divide the equation by \(a\).
 
x2+bax+ca=0
 
Move the constant to the right side.
 
x2+bax=ca
 
Add the square of one half of the coefficient of \(x\) on both sides.
 
x2+bax+b2a2=ca+b2a2
 
x+b2a2=ca+b24a2
 
x+b2a2=b24ac4a2
 
Taking square root on both sides.
 
x+b2a=±b24ac4a2
 
x+b2a=±b24ac2a
 
x=b2a±b24ac2a
 
x=b±b24ac2a
 
Therefore, the roots of \(ax^2 + bx + c = 0\) are x=b+b24ac2a and x=bb24ac2a.