How do you solve 2x^2 + x = 52x2+x=5?

1 Answer
Aug 16, 2015

x_(1,2) = (-1 +- sqrt(41))/4x1,2=1±414

Explanation:

You can solve this quadratic equation by using the quadratic formula, which tells you that for any general form quadratic equation

color(blue)(ax^2 + bx + c = 0)ax2+bx+c=0

the two roots of the equation take the form

color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)x1,2=b±b24ac2a

So, start by adding -55 to both sides of the equation to get

2x^2 + x - 5 = color(red)(cancel(color(black)(5))) - color(red)(cancel(color(black)(5)))

2x^2 + x -5 = 0

Notice that you have a=2, b=1, and c=-5. This means that the two solutions will be

x_(1,2) = (-1 +- sqrt(1^2 - 4 * 2 * (-5)))/(2 * 2)

x_(1,2) = color(green)((-1 +- sqrt(41))/4)

You can simplify this if you want to get

x_1 = (-1 + sqrt(41))/4 ~= 1.35078

and

x_2 = (-1 - sqrt(41))/4 ~= -1.85078