846/VB02. problem / Math - Solved Math Problems

MR-846 / 423c. problem

Using the formula $x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ for solutions of a quadratic equation $a x^{2} + b x + c = 0$ , solve the equation:

$2 x^{2} - 5 x - 25 = 0$

All Problems

Source: Vene T. Bogoslavov: Collection of Solved Problems #2 - 423.c.)

Algebra → Quadratic equations, inequalities and systems of equations → Quadratic equations

$2 x^{2} - 5 x - 25 = 0$

$a = 2; b = - 5; c = - 25$

$x_{1, 2} = \frac{- (- 5) \pm \sqrt{{(- 5)}^{2} - 4 \cdot 2 \cdot (- 25)}}{2 \cdot 2}$

$x_{1, 2} = \frac{5 \pm \sqrt{25 - 8 \cdot (- 25)}}{4}$

$x_{1, 2} = \frac{5 \pm \sqrt{25 + 200}}{4}$

$x_{1, 2} = \frac{5 \pm \sqrt{225}}{4}$

$x_{1, 2} = \frac{5 \pm 15}{4}$

$x_{1} = \frac{5 + 15}{4} = \frac{20}{4}$

$x_{1} = 5$

$x_{2} = \frac{5 - 15}{4} = - \frac{10}{4}$

$x_{2} = - \frac{5}{2} = - 2 \frac{1}{2}$

$x_{1} = 5; x_{2} = - \frac{5}{2}$

MathReference - Problems