Question

Add 20 to a number, square the sum and add the square of the number. The result is 848. The number is?

Answer 1

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