10(x+4)10(x+4)=16

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Solution for 10(x+4)10(x+4)=16 equation:


Simplifying
10(x + 4) * 10(x + 4) = 16

Reorder the terms:
10(4 + x) * 10(x + 4) = 16

Reorder the terms:
10(4 + x) * 10(4 + x) = 16

Reorder the terms for easier multiplication:
10 * 10(4 + x)(4 + x) = 16

Multiply 10 * 10
100(4 + x)(4 + x) = 16

Multiply (4 + x) * (4 + x)
100(4(4 + x) + x(4 + x)) = 16
100((4 * 4 + x * 4) + x(4 + x)) = 16
100((16 + 4x) + x(4 + x)) = 16
100(16 + 4x + (4 * x + x * x)) = 16
100(16 + 4x + (4x + x2)) = 16

Combine like terms: 4x + 4x = 8x
100(16 + 8x + x2) = 16
(16 * 100 + 8x * 100 + x2 * 100) = 16
(1600 + 800x + 100x2) = 16

Solving
1600 + 800x + 100x2 = 16

Solving for variable 'x'.

Reorder the terms:
1600 + -16 + 800x + 100x2 = 16 + -16

Combine like terms: 1600 + -16 = 1584
1584 + 800x + 100x2 = 16 + -16

Combine like terms: 16 + -16 = 0
1584 + 800x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(396 + 200x + 25x2) = 0

Factor a trinomial.
4((22 + 5x)(18 + 5x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(22 + 5x)' equal to zero and attempt to solve:

Simplifying
22 + 5x = 0

Solving
22 + 5x = 0

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

Add '-22' to each side of the equation.
22 + -22 + 5x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 5x = 0 + -22
5x = 0 + -22

Combine like terms: 0 + -22 = -22
5x = -22

Divide each side by '5'.
x = -4.4

Simplifying
x = -4.4

Subproblem 2
Set the factor '(18 + 5x)' equal to zero and attempt to solve:

Simplifying
18 + 5x = 0

Solving
18 + 5x = 0

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

Add '-18' to each side of the equation.
18 + -18 + 5x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 5x = 0 + -18
5x = 0 + -18

Combine like terms: 0 + -18 = -18
5x = -18

Divide each side by '5'.
x = -3.6

Simplifying
x = -3.6
Solution
x = {-4.4, -3.6}

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