Question

For what values of x is the trinomial 2x^2-x+55 equal to the square of binomial x+5

Answer 1

Answer:

x = 6 , 5. For these values of x they are equal.

Step-by-step explanation:

2x²  - x + 55 =(x +5)²

2x² - x + 55 = x² + 2*x*5 + 5²

2x² - x + 55 = x² + 10x + 25

2x² - x + 55 - x²  - 10x - 25 = 0

2x² - x² - x - 10x + 55 - 25 = 0

x² - 11x + 30 = 0

x² -6x - 5x  + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 6)(x - 5) = 0

x - 6 = 0 ;  x - 5 = 0

x = 6      ;      x = 5

Answer 2

Answer:

Step-by-step explanation:

$\displaystyle 2x^2-x+55=(x+5)^2 \\\\ 2x^2-x+55=x^2+10x+25 \\\\ 2x^2-x^2-x-10x+55-25=0 \\\\x^2-11x+30=0 \\\\ \left \{ {{x_1+x_2=11} \atop {x_1x_2=30 }} \right. => x_1=6 \ \ ; \ \ x_2=5$

$\huge \boldsymbol{ \mathfrak {Answe}r :} x_1=6 \ \ ; \ \ x_2=5 }$