How do you solve #x^2 - 45 = 0# using the quadratic formula?

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Answer 1 · 2017-07-15T14:22:46

See a solution process below:

To solve this problem using the quadratic formula we can rewrite the equation as:

#1x^2 + 0x - 45 = 0#

The quadratic formula states:

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

Substituting #1# for #a#; #0# for #b# and #-45# for #c# gives:

#x = (-0 +- sqrt(0^2 - (4 * 1 * -45)))/(2 * 1)#

#x = +- sqrt(0 - (-180))/2#

#x = +- sqrt(180)/2#

#x = +- sqrt(36 * 5)/2#

#x = +- (sqrt(36) * sqrt(5))/2#

#x = +- (6sqrt(5))/2#

#x = +- 3sqrt(5)#