Question

Stuck on this it's Algebra 2 12x^{3} -3x^{2} =0

Answer 1

Answer:

Exact Form:

x = 0, 1/4

Decimal Form:

x = 0, 0.25

Step-by-step 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)