SOLUTION: Show work please Solve the quadratic equations in questions 1 - 5 by factoring. 1.    x^2 - 49 = 0 2.    3x^3 - 12x = 0 3.    12x^2 + 14x + 12 = 18 4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Show work please Solve the quadratic equations in questions 1 - 5 by factoring. 1.    x^2 - 49 = 0 2.    3x^3 - 12x = 0 3.    12x^2 + 14x + 12 = 18 4      Log On


   

Question 1154246: Show work please
Solve the quadratic equations in questions 1 - 5 by factoring.
1.    x^2 - 49 = 0
2.    3x^3 - 12x = 0
3.    12x^2 + 14x + 12 = 18
4.    - x^3 + 22x^2 - 121x = 0
5.    x^2 - 4x = 5
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Too many for just one single posting.
Maybe say exactly what you have trouble to understand.

Picking just -x%5E3%2B22x%5E2-121x=0
-x%28x%5E2-22x%2B121%29=0, and recognize how the 22 and the 121 are related;
-x%28x-11%29%28x-11%29=0

Very obviously, either x=0 or x=11.



-
Look very carefully:
x%5E2-22x%2B121
x%5E2-22x%2B11%2A11
x%5E2-11x-11x%2B%28-11%29%28-11%29
%28x-11%29%28x-11%29
%28x-11%29%5E2
-
or if starting from the binomial to be multiplied,
%28x-11%29x-%28x-11%2911
x%5E2-11x-11x-%28-121%29
x%5E2-22x%2B121, the quadratic started from.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
x%5E2+-+49+=+0
x%5E2+-+7%5E2+=+0
%28x+-+7%29%28x%2B7%29+=+0
solutions: x=7, x=-7

2.

3x%5E3+-+12x+=+0
3x%28x%5E2+-+4%29+=+0
3x%28x%5E2+-+2%5E2%29+=+0
3x%28x+-+2%29%28x%2B2%29+=+0
solutions: x=0, x=2,x=-2

3.
12x%5E2+%2B+14x+%2B+12+=+18
12x%5E2+%2B+14x+%2B+12+-+18=0
12x%5E2+%2B+14x+-+6=0
2%286x%5E2+%2B+7x+-+3%29=0
2%286x%5E2-2x+%2B+9x+-+3%29=0
2%28%286x%5E2-2x%29+%2B+%289x+-+3%29%29=0
2%282x%283x-1%29+%2B+3%283x+-+1%29%29=0
2%282x+%2B+3%29%283x+-+1%29+=+0

solutions: x=-3%2F2, x=1%2F3

4.
+-+x%5E3+%2B+22x%5E2+-+121x+=+0
+-x%28+x%5E2+-+22x+%2B+121%29+=+0
+-x%28x+-+11%29%5E2+=+0
+-x%28x+-+11%29%28x%2B11%29+=+0
solutions: x=11, x=-11

5.
++x%5E2+-+4x+=+5
++x%5E2+-+4x+-5=0
++x%5E2%2Bx+-+5x+-5=0
+%28+x%5E2%2Bx%29+-+%285x+%2B5%29=0
+x%28+x%2B1%29+-+5%28x+%2B1%29=0
+%28+x+-+5%29%28x+%2B1%29=0
solutions: x=5, x=-1