How do you solve 2x^2 + x = 52x2+x=5?
1 Answer
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±√b2−4ac2a
So, start by adding
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
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