How do you solve $2 x^{2} - 11 x = 1$ $2x^2-11x=1$ ?

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Answer 1 · 2015-09-22T12:39:38

The solutions are
$x = \frac{11 + \sqrt{129}}{4}$ $color(blue)(x=(11+sqrt(129))/4$

$x = \frac{11 - \sqrt{129}}{4}$ $color(blue)(x=(11-sqrt(129))/4$

$2 x^{2} - 11 x = 1$ $2x^2−11x=1$

$2 x^{2} - 11 x - 1 = 0$ $2x^2−11x- 1=0$

The equation is of the form $a x^{2} + b x + c = 0$ $color(blue)(ax^2+bx+c=0$ where:
$a = 2, b = - 11, c = - 1$ $a=2, b=-11, c= -1$

The Discriminant is given by:
$Delta=b^2-4*a*c$
$= (-11)^2-(4*2* (-1))$
$= 121 +8=129$

The solutions are found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

$x = (-(-11)+-sqrt(129))/(2*2) = (11+-sqrt(129))/4$

The solutions are
$color(blue)(x=(11+sqrt(129))/4$

$color(blue)(x=(11-sqrt(129))/4$

How do you solve 2x^2-11x=12x2−11x=12x^2-11x=1?