Question

Xsquared-7x-34=10
Factorise and solve

Answer 1

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

Answer 2

`{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`

Answer:

x = -4 and 11

Hope you could understand.

If you have any query, feel free to ask.