Question

Solve (r? - 5)(x + 5) + 25​

Answer 1

Step-by-step explanation:

Solution of a quadratic equation by completing the square

Teacher: Is x + 10.x + 2 = 0 a quadratic equation or not?

Yogesh : Yes Sir, because it is in the form car? + bx + c = 0, ma

variable r is 2 and 'a' is non zero.

Teacher: Can you solve this equation ?

Yogesh : No Sir, because it is not possible to find the factors of 2

Teacher : Right, so we have to use another method to solve su

learn the method.

Let us add a suitable term to r? + 10 x so that the new ex

complete square.

If x + 10 x + k = (x + a)

then r' + 10 x + k = x + 2ax + a

.. 10 = 2 a and k = a?

by equating the coefficients for the variable x and consta

a=5. k= a = (5)2 = 25

ir + 10 x + 2 = (x + 5) - 25 + 2 = (x + 5) - 23

Now can you solve the equation x + 10 x + 2 = 0 ?

Rehana : Yes Sir, left side of the equation is now difference

can factorise it.

(r + 5) - ( 23 ) = 0

..(x + 5+ 23 )(x + 5 - 23 ) = 0

X + 5+ 23 = 0 or 3 + 5 - 23 = 0

.. r = -5- 23 or x = -5 + 23

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