An integral equation containing only one unknown (one variable) and the highest degree of the unknown term is 2 (quadratic)，which is called a quadratic equation of one variable.

The quadratic equation of one variable can be transformed into the general form \(ax²+bx+c=0\) (a≠0). Where ax² is called the quadratic term and a is the coefficient of the quadratic term;

bx is called the first-order term, b is the first-order coefficient; c is called the constant term.

Conditions for the establishment of quadratic equations in one variable

The establishment of the quadratic equation of one variable must satisfy three conditions at the same time:

① It is an integral equation, that is, both sides of the equal sign are integral, if there is a denominator in the equation; and the unknown number is on the denominator, then this equation is a fractional equation, not a quadratic equation of one variable, if there is a root in the equation, and the unknown number is in the root No., then this equation is not a quadratic equation (a irrational equation).

② It contains only an unknown number;

③ The maximum number of unknown items is 2.

The quadratic equation: \(ax^2+bx+c=0\) (a≠0, and a, b, c are constants)

Equation solution

\(x_1= \frac {-b+√[b^2-4ac]}{2a} \)

\(x_2= \frac {-b-√[b^2-4ac]}{2a} \)

a x^{2} + bx + c = 0

Quadratic coefficient a: 5

Quadratic coefficient b: 6

Constant term c: 9

Click "Solve Problem" and output the result

x_{1}: -0.6 + -1.2i

x_{2}: -0.6 + 1.2i

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