SOLUTION: Solve the following by either factoring, square root method, or quadratic formula. For each question determine which is the best method to use and why. Then solve the equation show

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve the following by either factoring, square root method, or quadratic formula. For each question determine which is the best method to use and why. Then solve the equation show      Log On


   

Question 1202969: Solve the following by either factoring, square root method, or quadratic formula. For each question determine which is the best method to use and why. Then solve the equation showing all work, and simplify your answers fully. Keep in mind that the quadratic formula is not always the most efficient method.
21-3(t-2)^2=9
x^2 + 12x-20=0
(x+3)(x-6)=-8
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1)
21-3%28t-2%29%5E2=9

The equation involves the square of an expression containing the variable, so probably the square root method is the most efficient.

12=3%28t-2%29%5E2
%28t-2%29%5E2=4
t-2=2 or t-2=-2
t=4 or t=0

ANSWERS: 0 and 4

(2)
x%5E2%2B12x-20=0

The equation is in the form needed for solving by factoring; but a quick look makes it appear that it does not factor. We can confirm that by seeing that b%5E2-4ac=144%2B80=224 is not a perfect square. So use the quadratic formula.

x=%28-12%2B-sqrt%28224%29%29%2F2

simplify as needed....

(3)
%28x%2B3%29%28x-6%29=-8

With "8" instead of 0 on the right, we can't solve this by the STANDARD factoring method. So put the equation in standard form and try factoring, and if that doesn't look good use the quadratic formula.

x%5E2-3x-18=-8
x%5E2-3x-10=0
%28x-5%29%28x%2B2%29=0
x=5 or x=-2

ANSWERS: -2 and 5

While this one can't be solved by the standard factoring method, it CAN be solved by factoring using some logical reasoning.

The product on the left is the product of two numbers whose difference is 9 and whose product is -8. A little mental arithmetic shows that the two numbers can be 8 and -1, or 1 and -8. Then

If x+3 = 8 then x = 5; if x+3 = 1 then x = -2

And again the two solutions are -2 and 5.