How do you solve #x^2 - 6x + 9 = 25#?
4 Answers
Explanation:
Given quadratic equation:
Explanation:
#"subtract 25 from both sides"#
#x^2-6x-16=0larrcolor(blue)"in standard form"#
#"the factors of "-16" which sum to "-6#
#"are "-8" and "+2#
#(x-8)(x+2)=0#
#"equate each factor to zero and solve for "x#
#x+2=0rArrx=-2#
#x-8=0rArrx=8#
Explanation:
Since we have a quadratic, let's set it equal to zero to find its zeroes. This can be done by subtracting
We now have
To factor this, let's do a little thought experiment:
What two numbers sum up to
This means we can factor this as
Setting both factors equal to zero, we get
Hope this helps!
Explanation:
Given:
#x^2-6x+9=25#
Note that both the left hand side and the right hand side are perfect squares, namely:
#(x-3)^2 = 5^2#
Hence:
#x-3=+-5#
So:
#x = 3+-5#
That is:
#x = 8" "# or#" "x = -2#