2x^2 - x = 10
=> 2x^2 - x - 10 = 0
=> 2x^2 - (5 - 4)x - 10 = 0
=> 2x^2 - 5x + 4x - 10 = 0
=> x(2x - 5) + 2(2x - 5) = 0
=> (2x - 5)(x + 2) = 0
Either, Or,
2x - 5 = 0 x + 2 = 0
=> 2x = 5 => x = - 2
=> x = 5/2
Answer:
[tex]x1 = \frac{5}{2} \: \: and \: x2 = - 2[/tex]
Step-by-step explanation:
So, our equation is:
2x² - x - 10 = 0
The numbers before x are a, b, and c
We must first find the discriminant which is equal to b² - 4*a*c
D = b² - 4 * a * c
Be careful here, b is -1 because we have minus before x and c is -10
D = (-1)² - 4*2*-10
D = 1 + 80
D = 81
Now we need to find the roots of the equation, since D is greater than 0, the roots are equal to (-b ± sqrt(D)) / 2*a
[tex]x1 = \frac{ -( - 1) + \sqrt{81} }{2 \times 2} = \frac{1 + 9}{4} = \frac{10}{4} = \frac{5}{2} [/tex]
and for x2 we will put minus:
[tex]x2 = \frac{ - ( - 1) - \sqrt{81} }{2 \times 2} = \frac{1 - 9}{4} = \frac{ - 8}{4} = -2 [/tex]
