6^3x+3=216^3-x find x pls
Answers
x3−216=0
Add 216
to both sides of the equation.
x3=216
Move 216
to the left side of the equation by subtracting it from both sides.
x3−216=0
Factor the left side of the equation.
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Rewrite 216
as 63
.
x3−63=0
Since both terms are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2)
where a=x and b=6
.
(x−6)(x2+x⋅6+62)=0
Simplify.
(x−6)(x2+6x+36)=0
Set x−6
equal to 0 and solve
Set the factor equal to 0
.
x−6=0
Add 6
to both sides of the equation.
x=6
Set x2+6x+36
equal to 0 and solve for x
Set the factor equal to
x2+6x+36=0
Use the quadratic formula to find the solutions.
−b±√b2−4(ac)2a
Substitute the values a=1
, b=6, and c=36 into the quadratic formula and solve for x
−6±√62−4⋅(1⋅36)2⋅1
Simplify
x=−3±3i√3
Simplify the expression to solve for the +
portion of the ±
x=−3+3i√3
Simplify the expression to solve for the −
portion of the ±
.
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Simplify the numerator.
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x=−6±6i√32⋅1
Multiply 2
by 1
.
x=−6±6i√32
Simplify −6±6i√32
.
x=−3±3i√3
Change the ±
to −
.
x=−3−3i√3
The final answer is the combination of both solutions.
x=−3+3i√3,−3−3i√3
The solution is the result of x−6=0
and x2+6x+36=0
.
x=6,−3+3i√3,−3−3i√3
Answer:
1
Step-by-step explanation:
