Question

quadratic equation(8x²+10x+56=7x²+67)​

Answer 1

Answer :

x = -11 , 1

Solution :

• Given : 8x² + 10x + 56 = 7x² + 67
• To find : x = ?

We have ;

=> 8x² + 10x + 56 = 7x² + 67

=> 8x² - 7x² + 10x + 56 - 67 = 0

=> x² + 10x - 11 = 0

=> x² + 11x - x - 11 = 0

=> x(x + 11) - (x + 11) = 0

=> (x + 11)(x - 1) = 0

=> Either (x + 11) = 0 or (x - 1) = 0

• If x + 11 = 0 , then x = -11 .

• If x - 1 = 0 , then x = 1 .

Hence x = -11 , 1 .

Alternative method :

Using quadratic formula .

We have ,

=> 8x² + 10x + 56 = 7x² + 67

=> 8x² - 7x² + 10x + 56 - 67 = 0

=> x² + 10x - 11 = 0

Comparing the quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;

a = 1

b = 10

c = -11

Now ,

The discriminant of the quadratic equation will be ;

=> D = b² - 4ac

=> D = 10² - 4•1•(-11)

=> D = 100 + 44

=> D = 144

Now ,

=> x = (-b ± √D)/2a

=> x = (-10 ± √144)/2•1

=> x = (-10 ± 12)/2

=> x = (-10 - 12)/2 , (-10 + 12)/2

=> x = -22/2 , 2/2

=> x = -11 , 1

Hence x = -11 , 1 .