Question

Solve this quadratic equation by completing the square. x2 + 10x = 26

Answer 1

ax^2+bx+c=d
to comlete teh square
minus c to both sides
make sure a=1, if not, divide both sides by a
take 1/2 of b, then square that and add that to both sides

so
x^2+10x=26
c is already over
a=1
b=10
10/2=5
5^2=25
add 25 both sides
x^2+10x+25=26+25
factor
(x+5)^2=51
sqrt both sides
x+5=+/-√51
minus 5
x=-5+/-√51

x=-5+√51 or -5-√51

Answer 2

x² + 10x = 26
x² + 10x + 25 = 26 + 25
x² + 5x + 5x + 25 = 51
x(x) + x(5) + 5(x) + 5(5) = 51
x(x + 5) + 5(x + 5) = 51
(x + 5)(x + 5) = 51
(x + 5)² = 51
x + 5 = ±√(51)
- 5 - 5
x = -5 ± √(51)
x = -5 + √(51) or x = -5 - √(51)