How do you solve #10x ^ { 2} - 20x - 350= 0#?

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Answer 1 · 2017-09-03T12:05:30

See a solution process below: #x = 7# and #x = -5#

First, to simplify the equation, divide each side of the equation by #color(red)(10)#:

#(10x^2 - 20x - 350)/color(red)(10) = 0/color(red)(10)#

#(10x^2)/color(red)(10) - (20x)/color(red)(10) - 350/color(red)(10) = 0#

#1x^2 - 2x - 35 = 0#

#x^2 - 2x - 35 = 0#

Next, factor the left side of the equation as:

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

Now, solve each term on the left side of the equation for #0# to find the solutions:

Solution 1:

#x - 7 = 0#

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

#x - 0 = 7#

#x = 7#

Solution 2:

#x + 5 = 0#

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

#x + 0 = -5#

#x = -5#

The Solutions Are: #x = 7# and #x = -5#