9x^2+18x-81=4

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Solution for 9x^2+18x-81=4 equation:


Simplifying
9x2 + 18x + -81 = 4

Reorder the terms:
-81 + 18x + 9x2 = 4

Solving
-81 + 18x + 9x2 = 4

Solving for variable 'x'.

Reorder the terms:
-81 + -4 + 18x + 9x2 = 4 + -4

Combine like terms: -81 + -4 = -85
-85 + 18x + 9x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-85 + 18x + 9x2 = 0

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

Divide each side by '9'.
-9.444444444 + 2x + x2 = 0

Move the constant term to the right:

Add '9.444444444' to each side of the equation.
-9.444444444 + 2x + 9.444444444 + x2 = 0 + 9.444444444

Reorder the terms:
-9.444444444 + 9.444444444 + 2x + x2 = 0 + 9.444444444

Combine like terms: -9.444444444 + 9.444444444 = 0.000000000
0.000000000 + 2x + x2 = 0 + 9.444444444
2x + x2 = 0 + 9.444444444

Combine like terms: 0 + 9.444444444 = 9.444444444
2x + x2 = 9.444444444

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9.444444444 + 1

Reorder the terms:
1 + 2x + x2 = 9.444444444 + 1

Combine like terms: 9.444444444 + 1 = 10.444444444
1 + 2x + x2 = 10.444444444

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10.444444444

Calculate the square root of the right side: 3.231786572

Break this problem into two subproblems by setting 
(x + 1) equal to 3.231786572 and -3.231786572.

Subproblem 1

x + 1 = 3.231786572 Simplifying x + 1 = 3.231786572 Reorder the terms: 1 + x = 3.231786572 Solving 1 + x = 3.231786572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.231786572 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.231786572 + -1 x = 3.231786572 + -1 Combine like terms: 3.231786572 + -1 = 2.231786572 x = 2.231786572 Simplifying x = 2.231786572

Subproblem 2

x + 1 = -3.231786572 Simplifying x + 1 = -3.231786572 Reorder the terms: 1 + x = -3.231786572 Solving 1 + x = -3.231786572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.231786572 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.231786572 + -1 x = -3.231786572 + -1 Combine like terms: -3.231786572 + -1 = -4.231786572 x = -4.231786572 Simplifying x = -4.231786572

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.231786572, -4.231786572}

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