x^2+x^2+9x+9=81

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Solution for x^2+x^2+9x+9=81 equation:


Simplifying
x2 + x2 + 9x + 9 = 81

Reorder the terms:
9 + 9x + x2 + x2 = 81

Combine like terms: x2 + x2 = 2x2
9 + 9x + 2x2 = 81

Solving
9 + 9x + 2x2 = 81

Solving for variable 'x'.

Reorder the terms:
9 + -81 + 9x + 2x2 = 81 + -81

Combine like terms: 9 + -81 = -72
-72 + 9x + 2x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-72 + 9x + 2x2 = 0

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

Divide each side by '2'.
-36 + 4.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 4.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 4.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4.5x + x2 = 0 + 36
4.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
4.5x + x2 = 36

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 36 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 36 + 5.0625

Combine like terms: 36 + 5.0625 = 41.0625
5.0625 + 4.5x + x2 = 41.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 41.0625

Calculate the square root of the right side: 6.408002809

Break this problem into two subproblems by setting 
(x + 2.25) equal to 6.408002809 and -6.408002809.

Subproblem 1

x + 2.25 = 6.408002809 Simplifying x + 2.25 = 6.408002809 Reorder the terms: 2.25 + x = 6.408002809 Solving 2.25 + x = 6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 6.408002809 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 6.408002809 + -2.25 x = 6.408002809 + -2.25 Combine like terms: 6.408002809 + -2.25 = 4.158002809 x = 4.158002809 Simplifying x = 4.158002809

Subproblem 2

x + 2.25 = -6.408002809 Simplifying x + 2.25 = -6.408002809 Reorder the terms: 2.25 + x = -6.408002809 Solving 2.25 + x = -6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -6.408002809 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -6.408002809 + -2.25 x = -6.408002809 + -2.25 Combine like terms: -6.408002809 + -2.25 = -8.658002809 x = -8.658002809 Simplifying x = -8.658002809

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.158002809, -8.658002809}

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