Question

9x^2+5x-1=0 use quadratic formula to solve for x

Answer 1

To solve the equation 9x^2+5x-1=0 using the quadratic formula, substitute the values of a, b, and c into the formula and simplify.

Step-by-step explanation:

To solve the equation 9x^2+5x-1=0 using the quadratic formula, we need to first identify the values of a, b, and c. In this equation, a=9, b=5, and c=-1. The quadratic formula is:

x = (-b±sqrt(b^2-4ac))/(2a)

Substituting the values, we get:

x = (-5±sqrt(5^2-4(9)(-1)))/(2(9))

Simplifying further, we have:

x = (-5±sqrt(25+36))/(18)

x = (-5±sqrt(61))/(18)

Therefore, the solutions for x are:

x = (-5+sqrt(61))/(18) and x = (-5-sqrt(61))/(18)

Answer 2

`9x^2+5x-1=0\\ \Delta=5^2-4\cdot 9\cdot (-1)=25+36=61\\ √(\Delta)=√(61)\\ x_1=(-5-√(61))/(2\cdot9)=-(5+√(61))/(18)\\ x_2=(-5+√(61))/(2\cdot9)=-(5-√(61))/(18)`