Answer:
x = 6, and x = -9
Explanation:
Area of a triangle = 1/2 base* height = 13 square inches
Slot in the values of the base and height
13 = 1/2 ( x + 7 ) * ( x - 4 )
Expand
13 = 1/2 (x^2 - 4x + 7x - 28)
collect like terms
13 = 1/2 ( x^2 + 3x - 28 )
cross multiply
13*2 = x^2 + 3x - 28
26 = x^2 + 3x - 28
Subtract 26 from both sides
0 = x^2 + 3x - 28 - 26
0 = x^2 + 3x - 28 - 54
rearrange
x^2 + 3x - 54 = 0
Two numbers which when multiplied gives -54 and when summed gives 3 are -6 and 9
x^2 - 6x + 9x - 54 = 0
x ( x - 6 ) + 9 (x - 6 ) = 0
(x - 6)(x + 9) = 0
x - 6 = 0
x = 6
x + 9 = 0
x = -9