845/VB02. problem / Math - Solved Math Problems

MR-845 / 423b. 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:

$x^{2} - 3 x - 28 = 0$

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

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

$x^{2} - 3 x - 28 = 0$

$a = 1; b = - 3; c = - 28$

$x_{1, 2} = \frac{- (- 3) \pm \sqrt{{(- 3)}^{2} - 4 \cdot 1 \cdot (- 28)}}{2 \cdot 1}$

$x_{1, 2} = \frac{3 \pm \sqrt{9 + 112}}{2}$

$x_{1, 2} = \frac{3 \pm \sqrt{121}}{2}$

$x_{1, 2} = \frac{3 \pm 11}{2}$

$x_{1} = \frac{3 + 11}{2} = \frac{14}{2}$

$x_{1} = 7$

$x_{2} = \frac{3 - 11}{2} = - \frac{8}{2}$

$x_{2} = - 4$

$x_{1} = 7; x_{2} = - 4$

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