(-3u^2-8u-4)+(4u^2-2u-6)=

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Solution for (-3u^2-8u-4)+(4u^2-2u-6)= equation:


Simplifying
(-3u2 + -8u + -4) + (4u2 + -2u + -6) = 0

Reorder the terms:
(-4 + -8u + -3u2) + (4u2 + -2u + -6) = 0

Remove parenthesis around (-4 + -8u + -3u2)
-4 + -8u + -3u2 + (4u2 + -2u + -6) = 0

Reorder the terms:
-4 + -8u + -3u2 + (-6 + -2u + 4u2) = 0

Remove parenthesis around (-6 + -2u + 4u2)
-4 + -8u + -3u2 + -6 + -2u + 4u2 = 0

Reorder the terms:
-4 + -6 + -8u + -2u + -3u2 + 4u2 = 0

Combine like terms: -4 + -6 = -10
-10 + -8u + -2u + -3u2 + 4u2 = 0

Combine like terms: -8u + -2u = -10u
-10 + -10u + -3u2 + 4u2 = 0

Combine like terms: -3u2 + 4u2 = 1u2
-10 + -10u + 1u2 = 0

Solving
-10 + -10u + 1u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -10u + 10 + u2 = 0 + 10

Reorder the terms:
-10 + 10 + -10u + u2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -10u + u2 = 0 + 10
-10u + u2 = 0 + 10

Combine like terms: 0 + 10 = 10
-10u + u2 = 10

The u term is -10u.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10u + 25 + u2 = 10 + 25

Reorder the terms:
25 + -10u + u2 = 10 + 25

Combine like terms: 10 + 25 = 35
25 + -10u + u2 = 35

Factor a perfect square on the left side:
(u + -5)(u + -5) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(u + -5) equal to 5.916079783 and -5.916079783.

Subproblem 1

u + -5 = 5.916079783 Simplifying u + -5 = 5.916079783 Reorder the terms: -5 + u = 5.916079783 Solving -5 + u = 5.916079783 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = 5.916079783 + 5 Combine like terms: -5 + 5 = 0 0 + u = 5.916079783 + 5 u = 5.916079783 + 5 Combine like terms: 5.916079783 + 5 = 10.916079783 u = 10.916079783 Simplifying u = 10.916079783

Subproblem 2

u + -5 = -5.916079783 Simplifying u + -5 = -5.916079783 Reorder the terms: -5 + u = -5.916079783 Solving -5 + u = -5.916079783 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = -5.916079783 + 5 Combine like terms: -5 + 5 = 0 0 + u = -5.916079783 + 5 u = -5.916079783 + 5 Combine like terms: -5.916079783 + 5 = -0.916079783 u = -0.916079783 Simplifying u = -0.916079783

Solution

The solution to the problem is based on the solutions from the subproblems. u = {10.916079783, -0.916079783}

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