Question

x^2-26x+160=0 completing the square

Answer 1

Answer:

x^2 - 26x + 160 = 0

look for the coefficient of x^2 and if it is not 1 then divide the equation by the coefficient of x^2 so as to make it 1.

next shift the constant to right hand side

take the coefficient of x divide it by 2, then square it and add to both sides of the given equation.

then solve for x

in the given example, a = 1, b = -26 and c = 160

[ a and b are the coefficients of x^2 and x respectively and c is the constant ]

x^2 - 26x + (13)^2 = -160 + (13)^2

=> x^2 - 26x +169 = -160 + 169

=> x^2 - 26x + 169 = 9

=> (x - 13)^2 = 9

=> x - 13 = √9

=> x - 13 = +3 and -3

=> x = 3 + 13 = 16 and x - 13 = -3 => x = 10

therefore x = 16 and x = 10 are the solutions

Answer 2

Answer:

⇢ x = 16

Step-by-step explanation:

⇢ x² - 26x + 160 = 0

Firstly, factor left hand side of equation:

⇢ (x - 10) (x - 16) = 0

Secondly, set factors to 0:

⇢ x - 10 = 0 or

⇢ x - 16 = 0

⇢ x = 10 or

⇢ x = 16

Therefore, this is the required answer.