(6x^2+16x+10)+(3x^2+6x)=

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Solution for (6x^2+16x+10)+(3x^2+6x)= equation:


Simplifying
(6x2 + 16x + 10) + (3x2 + 6x) = 0

Reorder the terms:
(10 + 16x + 6x2) + (3x2 + 6x) = 0

Remove parenthesis around (10 + 16x + 6x2)
10 + 16x + 6x2 + (3x2 + 6x) = 0

Reorder the terms:
10 + 16x + 6x2 + (6x + 3x2) = 0

Remove parenthesis around (6x + 3x2)
10 + 16x + 6x2 + 6x + 3x2 = 0

Reorder the terms:
10 + 16x + 6x + 6x2 + 3x2 = 0

Combine like terms: 16x + 6x = 22x
10 + 22x + 6x2 + 3x2 = 0

Combine like terms: 6x2 + 3x2 = 9x2
10 + 22x + 9x2 = 0

Solving
10 + 22x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
1.111111111 + 2.444444444x + x2 = 0

Move the constant term to the right:

Add '-1.111111111' to each side of the equation.
1.111111111 + 2.444444444x + -1.111111111 + x2 = 0 + -1.111111111

Reorder the terms:
1.111111111 + -1.111111111 + 2.444444444x + x2 = 0 + -1.111111111

Combine like terms: 1.111111111 + -1.111111111 = 0.000000000
0.000000000 + 2.444444444x + x2 = 0 + -1.111111111
2.444444444x + x2 = 0 + -1.111111111

Combine like terms: 0 + -1.111111111 = -1.111111111
2.444444444x + x2 = -1.111111111

The x term is 2.444444444x.  Take half its coefficient (1.222222222).
Square it (1.493827160) and add it to both sides.

Add '1.493827160' to each side of the equation.
2.444444444x + 1.493827160 + x2 = -1.111111111 + 1.493827160

Reorder the terms:
1.493827160 + 2.444444444x + x2 = -1.111111111 + 1.493827160

Combine like terms: -1.111111111 + 1.493827160 = 0.382716049
1.493827160 + 2.444444444x + x2 = 0.382716049

Factor a perfect square on the left side:
(x + 1.222222222)(x + 1.222222222) = 0.382716049

Calculate the square root of the right side: 0.618640484

Break this problem into two subproblems by setting 
(x + 1.222222222) equal to 0.618640484 and -0.618640484.

Subproblem 1

x + 1.222222222 = 0.618640484 Simplifying x + 1.222222222 = 0.618640484 Reorder the terms: 1.222222222 + x = 0.618640484 Solving 1.222222222 + x = 0.618640484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + x = 0.618640484 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = 0.618640484 + -1.222222222 x = 0.618640484 + -1.222222222 Combine like terms: 0.618640484 + -1.222222222 = -0.603581738 x = -0.603581738 Simplifying x = -0.603581738

Subproblem 2

x + 1.222222222 = -0.618640484 Simplifying x + 1.222222222 = -0.618640484 Reorder the terms: 1.222222222 + x = -0.618640484 Solving 1.222222222 + x = -0.618640484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + x = -0.618640484 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + x = -0.618640484 + -1.222222222 x = -0.618640484 + -1.222222222 Combine like terms: -0.618640484 + -1.222222222 = -1.840862706 x = -1.840862706 Simplifying x = -1.840862706

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.603581738, -1.840862706}

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