# Solve the following quadratic function?

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To solve a quadratic function, you need to follow these steps:

- Write the quadratic function in the form ( ax^2 + bx + c = 0 ).
- Use the quadratic formula ( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} ) to find the solutions.

For example, let's solve the quadratic function ( 2x^2 - 5x + 2 = 0 ):

- Given quadratic function: ( 2x^2 - 5x + 2 = 0 )
- Using the quadratic formula: ( x = \frac{{-(-5) \pm \sqrt{{(-5)^2 - 4(2)(2)}}}}{2(2)} ) ( x = \frac{{5 \pm \sqrt{{25 - 16}}}}{4} ) ( x = \frac{{5 \pm \sqrt{9}}}{4} ) ( x = \frac{{5 \pm 3}}{4} )

The solutions are: ( x_1 = \frac{{5 + 3}}{4} = \frac{8}{4} = 2 ) ( x_2 = \frac{{5 - 3}}{4} = \frac{2}{4} = 0.5 )

So, the solutions to the quadratic function ( 2x^2 - 5x + 2 = 0 ) are ( x = 2 ) and ( x = 0.5 ).

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