Answer:
Exact Form:
x = 0, 1/4
Decimal Form:
x = 0, 0.25
Explanation:
Step 1: Factor 3x^2 out of 12x^3 - 3x^2
Factor 3x^2 out of 12x^3:
3x^2 (4x) - 3x^2 = 0
Factor 3x^2 out of -3x^2:
3x^2 (4x) + 3x^2 (-1) = 0
Factor 3x^2 out of -3x^2 (4x) + 3x^2 (-1) :
3x^2 (4x-1) = 0
Step 2: Divide each term by 3 and simpify
divide each term in 3x^2 (4x-1) = 0 by 3.
3x^2 (4x-1) / 3 = 0 / 3
simplify 3x^2 (4x-1) / 3.
Cancel the common factors.
3 x^2 (4x -1) / 3 = 0 / 3
divide x^2 (4x-1) by 1.
x^2 (4x-1) / 3 = 0 / 3
Apply the Distributive Property
Reorder.
Rewrite using the commutative property of multiplication.
4x^2 x + x^2 · -1 = 0 / 3
Move -1 to the left of x^2
4x^2 x -1 · x^2 = 0 / 3
Simplify each term
multiply x^2 by x^2 by adding the exponents.
Move x
4 (x · x^2) -1 · x^2= 0 / 3
Multiply x by x^2
Rase x to the power of 1.
4 (x^1 · x^2) -1 · x^2= 0 / 3
Use the power rule a^m a^n = a^m+n to combine exponents
4x^1+2 -1 · x^2= 0 / 3
Add 1 and 2.
4x^3 -1 · x^2= 0 / 3
Rewrite -1x^2 as -x^2.
4x^3 -x^2= 0 / 3
Divide 0 by 3
4x^3 -x^2= 0
Step 3: Factor x^2 out of 4x^3 -x^2.
Factor x^2 out of 4x^3
x^2 (4x) -x^2 = 0
Factor x^2 out of -x^2
x^2 (4x) x^2 · -1 = 0
Factor x^2 out of x^2 (4x) x^2 · -1
x^2 (4x -1) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0
x^2 = 0
4x -1 = 0
Set x^2 equal to 0 and solve for x
x = 0
Set 4x -1 equal to 0 and solve for x
x = 1/4
The final solution is all the values that make x^2 (4x-1) = 0 true
x= (0, 1/4)