Answer:
Exact Form:
x = 0, 1/4
Decimal Form:
x = 0, 0.25
Step-by-step explanation:
<u>Step 1: Factor 3x^2 out of 12x^3 - 3x^2 </u>
Factor 3x^2 out of 12x^3:
<em> 3x^2 (4x) - 3x^2 = 0</em>
Factor 3x^2 out of -3x^2:
<em> 3x^2 (4x) + 3x^2 (-1) = 0</em>
Factor 3x^2 out of -3x^2 <em>(4x) + 3x^2 (-1) </em>:
<em> 3x^2 (4x-1) = 0</em>
<em />
<u>Step 2: Divide each term by 3 and simpify</u>
<u></u>
divide each term in 3x^2 (4x-1) = 0 by 3.
3x^2 (4x-1) / 3 = 0 / 3
<em>simplify 3x^2 (4x-1) / 3.</em>
<em />
<em>Cancel the common factors.</em>
<u><em>3</em></u><em> </em>x^2 (4x -1) / <em><u>3</u></em> = 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
<u>Step 3: Factor x^2 out of 4x^3 -x^2.</u>
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)
