(40+x^2)(30+x^2)=3000

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Solution for (40+x^2)(30+x^2)=3000 equation: 


Simplifying
(40 + x2)(30 + x2) = 3000

Multiply (40 + x2) * (30 + x2)
(40(30 + x2) + x2(30 + x2)) = 3000
((30 * 40 + x2 * 40) + x2(30 + x2)) = 3000
((1200 + 40x2) + x2(30 + x2)) = 3000
(1200 + 40x2 + (30 * x2 + x2 * x2)) = 3000
(1200 + 40x2 + (30x2 + x4)) = 3000

Combine like terms: 40x2 + 30x2 = 70x2
(1200 + 70x2 + x4) = 3000

Solving
1200 + 70x2 + x4 = 3000

Solving for variable 'x'.

Reorder the terms:
1200 + -3000 + 70x2 + x4 = 3000 + -3000

Combine like terms: 1200 + -3000 = -1800
-1800 + 70x2 + x4 = 3000 + -3000

Combine like terms: 3000 + -3000 = 0
-1800 + 70x2 + x4 = 0

Factor a trinomial.
(-90 + -1x2)(20 + -1x2) = 0


Subproblem 1
Set the factor '(-90 + -1x2)' equal to zero and attempt to solve:

Simplifying
-90 + -1x2 = 0

Solving
-90 + -1x2 = 0

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

Add '90' to each side of the equation.
-90 + 90 + -1x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -1x2 = 0 + 90
-1x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-1x2 = 90

Divide each side by '-1'.
x2 = -90

Simplifying
x2 = -90

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(20 + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + -1x2 = 0

Solving
20 + -1x2 = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x2 = 0 + -20
-1x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-1x2 = -20

Divide each side by '-1'.
x2 = 20

Simplifying
x2 = 20

Take the square root of each side:
x = {-4.472135955, 4.472135955}
Solution
x = {-4.472135955, 4.472135955}

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