Solve and check. x^2 + 8x + 16 = 13

Question

Solve.

x² + 8x + 16 = 13

Answer 1

Given equation x ^2 + 8 x + 16 = 13.

x ^2 + 8 x + 16 - 13 = 0

x ^2 + 8 x + 3= 0

Compare it to quadratic form a x^2 + b x + c = 0.

a = 1, b =8, c = 3.

x = [- b ± √(b ^2 - 4ac]/2a

x = [- 8 ± √(64 - 12)]/2

x = [- 8 ± √52]/2

x = [- 8 ± 2√13 ]/2

x =[- 4 ± √13 ]

x = - 4 + √13  and  x = - 4 - √13.

Solution :    x = - 4 + √13  and  x = - 4 - √13.

Check :-

(1)  x = - 4 + √13

(- 4 + √13) ^2 + 8 (- 4 + √13 ) + 16 = 13

( a + b )^2 = a ^2 + 2ab + b ^2.

16 - 8√13 + 13 - 32 + 8√13 + 16 = 13

45 - 32 = 13

13 = 13.

(2)   x = -  4 - √13

(- 4 -√13 ) ^2 + 8 ( - 4 - √13 ) + 16 = 13

( a - b ) ^2 = a ^2 - 2ab + b ^2.

16 + 8√13 + 13 - 32 - 8 √13 + 16 = 13

45 - 32 = 13

13 =13.

Above statement is true.

So the value of x = - 4 + √13  and  x = - 4 - √13 are the solutions of the original equation.