(7+x)(7+x)(7+x)-343=0

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Solution for (7+x)(7+x)(7+x)-343=0 equation: 


Simplifying
(7 + x)(7 + x)(7 + x) + -343 = 0

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x))(7 + x) + -343 = 0
((7 * 7 + x * 7) + x(7 + x))(7 + x) + -343 = 0
((49 + 7x) + x(7 + x))(7 + x) + -343 = 0
(49 + 7x + (7 * x + x * x))(7 + x) + -343 = 0
(49 + 7x + (7x + x2))(7 + x) + -343 = 0

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2)(7 + x) + -343 = 0

Multiply (49 + 14x + x2) * (7 + x)
(49(7 + x) + 14x * (7 + x) + x2(7 + x)) + -343 = 0
((7 * 49 + x * 49) + 14x * (7 + x) + x2(7 + x)) + -343 = 0
((343 + 49x) + 14x * (7 + x) + x2(7 + x)) + -343 = 0
(343 + 49x + (7 * 14x + x * 14x) + x2(7 + x)) + -343 = 0
(343 + 49x + (98x + 14x2) + x2(7 + x)) + -343 = 0
(343 + 49x + 98x + 14x2 + (7 * x2 + x * x2)) + -343 = 0
(343 + 49x + 98x + 14x2 + (7x2 + x3)) + -343 = 0

Combine like terms: 49x + 98x = 147x
(343 + 147x + 14x2 + 7x2 + x3) + -343 = 0

Combine like terms: 14x2 + 7x2 = 21x2
(343 + 147x + 21x2 + x3) + -343 = 0

Reorder the terms:
343 + -343 + 147x + 21x2 + x3 = 0

Combine like terms: 343 + -343 = 0
0 + 147x + 21x2 + x3 = 0
147x + 21x2 + x3 = 0

Solving
147x + 21x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(147 + 21x + x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(147 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
147 + 21x + x2 = 0

Solving
147 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-147' to each side of the equation.
147 + 21x + -147 + x2 = 0 + -147

Reorder the terms:
147 + -147 + 21x + x2 = 0 + -147

Combine like terms: 147 + -147 = 0
0 + 21x + x2 = 0 + -147
21x + x2 = 0 + -147

Combine like terms: 0 + -147 = -147
21x + x2 = -147

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -147 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -147 + 110.25

Combine like terms: -147 + 110.25 = -36.75
110.25 + 21x + x2 = -36.75

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = -36.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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