Question

Find all values of $x$ such that $2x^2 +9x - 5=0$. If you find more than one value, then list your solutions in increasing order, separated by commas.

Answer 1

The given equation is a quadratic equation and we can find the solutions of the quadratic equation using the quadratic formula.

The Quadratic formula is:

`x= \frac{-b+- \sqrt{ b^(2)-4ac } }{2a}`

Here,

b = coefficient of x term = 9

a = coefficient of squared term = 2

c = constant term = -5

Using the values of, we get:

`x=(-9+-√(81-4(2)(-5)))/(2(2))\\\\x=(-9+-11)/(4)\\\\x= (-9-11)/(4)=-5, x= (-9+11)/(4)= (1)/(2)=0.5`

Thus the values of x satisfying the given equation are x = -5, x = 0.5