How do you solve #a^ { 2} + 7a - 14= 5a - 6#?

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Answer 1 · 2017-10-18T11:57:32

#(a +4) xx (a-2) # Combine terms and factor into binomials

First combine terms putting all the terms equal to zero.

# a^2 +7a -5a -14 + 6 = 5a-5a -6 +6# This gives

# a^2 + 2a - 8 = 0#

The -8 indicates that one of the terms must be positive and the other negative.

The +2a indicates that the positive term must be larger and that there is a difference of 2 between the terms.

Factors of 8 are # 2 xx 4 # and # 1 xx 8#

2 and 4 have a difference of 2 so 2, 4 work

The 4 must be the positive value and the 2 the negative value.

# ( a + 4) xx ( a -2) = 0#
Now solve for each factor

# a + 4 = 0 # subtract 4 from each side

# a + 4 -4 = 0 - 4 #

# a = -4 #

# a -2 = 0 # add 2 to both sides

# a -2 + 2 = 0 +2 #

a = 2