How do you solve $2 x^{2} - 11 x + 5 = 0$ $2x^2 - 11x + 5 = 0$ ?

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Answer 1 · 2015-07-10T17:15:39

The solutions for the equation are:
$x = \frac{1}{2}, x = 5$ $color(blue)(x=1/2, x=5$

$2 x^{2} - 11 x + 5 = 0$ $2x^2 - 11x +5 = 0$

We can first factorise the equation by splitting the middle term and then find the solutions:

$2 x^{2} - 11 x + 5 = 0$ $2x^2 -color(blue)( 11x) +5 = 0$

$2 x^{2} - 10 x - 1 x + 5 = 0$ $2x^2 color(blue)(- 10x - 1x) +5 = 0$

$2 x (x - 5) - 1 (x - 5) = 0$ $2x(x-5) - 1(x -5) = 0$

$(2 x - 1) (x - 5) = 0$ $color(blue)((2x - 1)(x-5) = 0$

Now we equate each of the two terms with zero to find the solutions:
$2 x - 1 = 0, x = \frac{1}{2}$ $color(blue)(2x - 1 = 0, x = 1/2)$

$x - 5 = 0, x = 5$ $color(blue)(x-5=0, x=5$

How do you solve 2x^2 - 11x + 5 = 02x2−11x+5=02x^2 - 11x + 5 = 0?