Answer:
x = 8 or x = -2
Step-by-step 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:
x = 8,-2
Step-by-step explanation:
First, complete the square on LHS (Left-Handed Side).
[tex]\displaystyle \large{x^2-6x+9=(x-3)^2}[/tex]
Make sure to recall the perfect square formula. Rewrite another equation with (x-3)² instead.
[tex]\displaystyle \large{(x-3)^2 = 25}[/tex]
Square both sides of equation.
[tex]\displaystyle \large{\sqrt{(x-3)^2}=\sqrt{25}}[/tex]
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.
[tex]\displaystyle \large{x-3=\pm \sqrt{25}}\\ \displaystyle \large{x-3=\pm 5}\\ \displaystyle \large{x=\pm 5+3}[/tex]
Therefore, x = 5+3 or x = -5+3
Thus, x = 8,-2
The method above is called completing the square method.
