That a bit tricky question :-
so let's do the question in small steps :)
Let a number be x.
Part 1 :-
Add 20 to a number
here we have to take the sum of 20 and x so equation formed :-
20 + x
Part 2 :-
square the sum
So in this we have to square 20+x , so equation formed.
(20 + x)²
Part 3 :-
add the square of the number
So in this part we have to add (20 + x)² and x's square i.e x² , so equation formed :-
(20 + x)² + x²
Part 4 :-
The result is 848
So in this we the expression which came in previous part is equal to 848, so equation formed:-
(20 + x)² + x² = 848
Part 5:-
To find value of x
So simplify the whole equation and we will get x.
➻ (20 + x)² + x² = 848
➻(20² + x² + 2 × x × 20) + x² = 848
➻(400 + x² + 2 × x × 20) + x² = 848
➻(400 + x² + 40 × x ) + x² = 848
➻(400 + x² + 40x ) + x² = 848
➻400 + x² + 40x + x² = 848
➻400 + 40x + 2x² = 848
➻2(200 + 20x + x²) = 848
➻200 + 20x + x² = 848/2
➻200 + 20x + x² = 424
➻20x + x² = 424 - 200
➻20x + x² = 224
➻x² + 20x - 224 = 0
➻x² +28x - 8x - 224 = 0
➻x( x + 28) - 8 (x + 28)
➻(x - 8)(x + 28)
Two solutions:-
x = 8
x = -28
