Question

4. Solve by completing
the
square method
x² - 3 x-10=0​

Answer 1

Answer:

x = 5 and x = -2

Step-by-step explanation:

$x^{2} - 3x-10=0\\x^{2} - 3x = 10\\x^{2} - 2*x*\frac{3}{2} = 10\\x^{2} - 2*x*\frac{3}{2} +(\frac{3}{2})^{2} = 10 + (\frac{3}{2})^{2}\\(x - \frac{3}{2})^{2} = 10 + \frac{9}{4}\\(x - \frac{3}{2})^{2} = \frac{40 +9}{4} = \frac{49}{4}\\(x - \frac{3}{2}) = \±\sqrt{ \frac{49}{4}}\\x - \frac{3}{2} = \±\frac{7}{2}\\x = \±\frac{7}{2} + \frac{3}{2}$

$x = +\frac{7}{2} + \frac{3}{2} \ and \ x = -\frac{7}{2} + \frac{3}{2}\\\\x = \frac{10}{2} \ and \ x = -\frac{4}{2}\\\\x = 5 \ and \ x = -2$

Therefore x = 5 and -2