How do you solve #3x ^ { 2} + 7x - 8= - 10#?

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Answer 1 · 2017-07-04T02:57:42

See a solution process below:

First, add #color(red)(10)# to each side of the equation to put this into true quadratic form while keeping the equation balanced:

#3x^2 + 7x - 8 + color(red)(10) = -10 + color(red)(10)#

#3x^2 + 7x + 2 = 0#

We can now factor the left side of the equation as:

#(3x + 1)(x + 2) = 0#

Now, we solve each term on the left side of the equation to obtain the answer:

Solution 1)

#3x + 1 = 0#

#3x + 1 - color(red)(1) = 0 - color(red)(1)#

#3x + 0 = -1#

#3x = -1#

#(3x)/color(red)(3) = -1/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -1/3#

#x = -1/3#

Solution 2)

#x + 2 = 0#

#x + 2 - color(red)(2) = 0 - color(red)(2)#

#x + 0 = -2#

#x = -2#

The solutions are: #x = -1/3# and #x = -2#