How do you solve #x^ { 2} - 9x + 46= 4x + 10#?

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Answer 1 · 2017-09-02T17:46:24

See a solution process below:

First, subtract #color(red)(4x)# and #color(blue)(10)# from each side of the equation to put this equation into standard form:

#x^2 - 9x - color(red)(4x) + 46 - color(blue)(10) = 4x - color(red)(4x) + 10 - color(blue)(10)#

#x^2 + (-9 - color(red)(4))x + (46 - color(blue)(10)) = 0 + 0#

#x^2 + (-13)x + 36 = 0#

#x^2 - 13x + 36 = 0#

We can factor the left side of the equation as:

#(x - 4)(x - 9) = 0#

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

Solution 1:

#x - 4 = 0#

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

#x - 0 = 4#

#x = 4#

Solution 2:

#x - 9 = 0#

#x - 9 + color(red)(9) = 0 + color(red)(9)#

#x - 0 = 9#

#x = 9#

The Solutions Are: #x = 4# and #x = 9#