How do you solve #-9x^{2}+6x-1=0#?

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Answer 1 · 2018-01-14T12:44:50

See a solution process below:

We can use the quadratic equation to solve this problem:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(-9)# for #color(red)(a)#

#color(blue)(6)# for #color(blue)(b)#

#color(green)(-1)# for #color(green)(c)# gives:

#x = (-color(blue)(6) +- sqrt(color(blue)(6)^2 - (4 * color(red)(-9) * color(green)(-1))))/(2 * color(red)(-9))#

#x = (-color(blue)(6) +- sqrt(color(blue)(36) - 36))/-18#

#x = (-color(blue)(6) +- sqrt(0))/-18#

#x = (-color(blue)(6) +- 0)/-18#

#x = (-color(blue)(6))/-18#

#x = 1/3#