How do you solve #7x ^ { 2} - 33x + 20= 0#?

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Answer 1 · 2017-06-18T23:10:32

See a solution process below:

First, we can play with factors of #7# and #20# to factor the quadratic as:

#(7x - 5)(x - 4) = 0#

We can now solve each term on the left side of the equation for #0# to find the solutions:

Solution 1)

#7x - 5 = 0#

#7x - 5 + color(red)(5) = 0 + color(red)(5)#

#7x - 0 = 5#

#7x = 5#

#(7x)/color(red)(7) = 5/color(red)(7)#

#(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 5/7#

#x = 5/7#

Solution 2)

#x - 4 = 0#

#x - 4 + color(red)(4) = 0 + color(red)(4)#

#x - 0 = 4#

#x = 4#

The solutions are: #x = 5/7# and #x = 4#