1. Simplify the quadratic equation into its standard form
Formula : ax^2+bx+c=0
Subtract from both sides:
x^2-10x+25=51
x^2-10x+25-51=0
x^2-10x-26=0
Use the standard form, ax^2+bx+c=0, to find the coefficients of our equation.
x^2-10x-26=0
a=1
b=-10
c=-26
The quadratic formula gives us the roots for ax^2+bx+c=0, in which a, b and c are numbers (or coefficients), as follows :
x=(-b±sqrt(b^2-4ac))/(2a)
to get the result :
x=(10±sqrt(204))/2
Simplify 204 by finding its prime factors:
The prime factorization of 204 is 2^2*3*17
x_2=-2.141
Answer:
x = 5 ± √51
Step-by-step explanation:
x² - 10x + 25 = 51
x² - 10x + 25 - 51 = 51 - 51
x² - 10x - 26 = 0
Factors with a product of -26 and a sum of -10:
NONE! Solve by completing the square (see attachment)
Step 1: Rearrange
x² - 10x + 25 = 51
x² - 10x = 26
Step 2: Add (b/2)² to both sides
x² - 10x + (-10/2)² = 26 + (-10/2)²
x² - 10x + 25 = 51
Step 3: Factor and solve
(x - 5)² = 51
x - 5 = √51
x = 5 ± √51
