How do you solve #7x^2-5=2x+9x^2# using the quadratic formula?

1 Answer
Aug 10, 2017

Answer:

#x=-(1+3i)/2,# #x=-(1-3i)/2#

Refer to the explanation for the process.

Explanation:

Quadratic Equation

First combine like terms and rewrite the equation in standard form.

#7x^2-5=2x+9x^2#

Move all terms to the left side.

#7x^2-5-2x-9x^2=0#

Simplify.

#-2x^2-5-2x-9x^2=0#

Rewrite in standard form: #ax^2+bx+c=0#.

#-2x^2-2x-5=0#,

where #a=-2#, #b=-2#, and #c=-5#.

Quadratic Formula

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

Plug in the known values.

#x=(-(-2)+-sqrt((-2)^2-4*-2*-5))/(2*-2)#

Simplify.

#x=(2+-sqrt(-36))/(-4)#

Simplify.

#x=-(2+-6i)/(4)#

#x=-(2+6i)/(4),# #(-2-36i)/(4)#

Reduce.

#x=-(color(red)cancel(color(black)(2^1))+color(red)cancel(color(black)(6^(3)))i)/color(red)cancel(color(black)(4^2)),# #-(color(red)cancel(color(black)(2^1))-color(red)cancel(color(black)(6^(3)))i)/color(red)cancel(color(black)(4^2)),#

#x=-(1+3i)/2,# #x=-(1-3i)/2#