Problem 1
2x² = 200
/2 /2 divide both sides by 2
x² = 100
√ √ get square root of both sides
x = + or - 10
Problem 2 easier to factor
x² - 4x -5
what times to -5 and adds to -4? -5 and 1
(x-5) (x+1) = 0
x = 5 and -1
Problem 3 Is a difference of squares
x² -144
diff of squares factor easily
(x+12)(x-12)
x = -12, +12
Problem 4 use radical
(x-4)² = 25
√ √ square root each side
x-4 = + - 5
+ 4 + 4 add 4 to both sides
x = + 5 + 4 and -5 +4
x = 9 and -1
Problem 5 factor
x² -16x + 64 = 0
what times to +64 and adds to -16? -8 and -8
x = 8
Part 2
Karen got the right answers but did so much more work than necessary.
on number one by dividing out the coefficient 2 you notice you have two squares so you can square root. On problem 2 you should always try factoring before completing the square of quadratic formula