Question

What are the values of x in the equation x2 – 6x + 9 = 25? x = –2 or x = 8 x = –1 or x = –11 x = 1 or x = 11 x = 2 or x = –8

Answer 1

x = 8 or x = -2

Explanation:

x^2 - 6x + 9 = 25

x^2 - 6x - 16 = 0

The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a

with a = 1

b = -6

c = -16

substitute in the formula

x = [-(-6) +/- √(-6^2 - 4(1)(-16))]/2(1)

x = [6 +/- √(36 + 64)]/2

x = [6 +/- √10]/2

x = [6 +/- 10]/2

x1 = [6 + 10]/2 = 16/2 = 8

x2 = [6 - 10]/2 = -4/2 = -2

Answer 2

x = 8,-2

Explanation:

First, complete the square on LHS (Left-Handed Side).

`\displaystyle \large{x^2-6x+9=(x-3)^2}`

Make sure to recall the perfect square formula. Rewrite another equation with (x-3)² instead.

`\displaystyle \large{(x-3)^2 = 25}`

Square both sides of equation.

`\displaystyle \large{√((x-3)^2)=√(25)}`

Because x² = (-x)² which means that it’s possible for x to be negative. Thus, write plus-minus beside √25 and cancel square of LHS.

`\displaystyle \large{x-3=\pm √(25)}\\ \displaystyle \large{x-3=\pm 5}\\ \displaystyle \large{x=\pm 5+3}`

Therefore, x = 5+3 or x = -5+3

Thus, x = 8,-2

The method above is called completing the square method.