Does the equation [tex]2x^2 + x - 1 = 9[/tex] have any real solutions? If so, what are they?

2 x 2 + x − 1 = 9 2 x 2 + x − 1 − 9 = 0 2 x 2 + x − 5 x + 5 x − 10 = 0 2 x 2 − 4 x + 5 x − 10 = 0 2 x ( x − 2 ) + 5 ( x − 2 ) = 0 ( x − 2 ) ( 2 x + 5 ) = 0 x − 2 = 0 or 2 x + 5 = 0 x = 2 or 2 x = − 5 x = 2 or x = − 2 5 ​ A n s w er : x = 2 or x = − 2 5 ​

Answered by Lilith | 2024-06-10

2x^2 + x – 1 = 9 2x^2+x-1-9=0 2x^2+x-10=0 a=2 b=1 c=-10
Delta=b^2-4ac Delta=1-4 2 (-10) delta=1+80 delta=81 rad 81=9
x1=-b-rad 81 /2a x1=-1-9/2*2 x1=-10/4 x1=-5/2
x2= -b+rad 81 /2a x2=-1+9/2*2 x2=8/4 x2=2

Answered by ioana123 | 2024-06-10

The equation 2 x 2 + x − 1 = 9 has two real solutions: x = 2 and x = − 2 5 ​ . This was determined by converting the equation into standard form and applying the quadratic formula. The positive discriminant confirms that there are indeed two real solutions.
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Answered by Lilith | 2025-06-16