[tex] {x}^{2} - 7x - 34 = 10 \\ = > {x }^{2} - 7x - 34 - 10 = 0 \\ = > {x}^{2} - 7x - 44 = 0 \\ = > {x}^{2} - 11x + 4x - 44 = 0 \\ = > x(x - 11) + 4(x - 11) = 0 \\ = > (x + 4)(x - 11) = 0 \\ = > x = - 4 \: \: and \: \: 11[/tex]
Answer:
x = -4 and 11
Hope you could understand.
If you have any query, feel free to ask.
Step-by-step explanation:
x² - 7x - 34 = 10
x² - 7x - 44 = 0
factorization by completing the square.
we know that (x + c)² = x² + 2cx + c²
so, what do we have ?
x² done
2cx = -7x
2c = -7
c = -7/2 done
but that means we should have (-7/2)² = 49/4 at the end. and we have -44 instead.
-44 = -176/4 (-44×4/4)
the difference between 49/4 and -176/4 is -225/4.
so, the equation with the completed square is transformed
(x - 7/2)² - 225/4 = 0
or
(x - 7/2)² = 225/4
and now we can solve based on this by creating the square root.
x - 7/2 = 15/2 or -15/2
x1 = 15/2 + 7/2 = 22/2 = 11
x2 = -15/2 + 7/2 = -8/2 = -4
