9x^2-36x-35=0

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Solution for 9x^2-36x-35=0 equation:


Simplifying
9x2 + -36x + -35 = 0

Reorder the terms:
-35 + -36x + 9x2 = 0

Solving
-35 + -36x + 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'.
-3.888888889 + -4x + x2 = 0

Move the constant term to the right:

Add '3.888888889' to each side of the equation.
-3.888888889 + -4x + 3.888888889 + x2 = 0 + 3.888888889

Reorder the terms:
-3.888888889 + 3.888888889 + -4x + x2 = 0 + 3.888888889

Combine like terms: -3.888888889 + 3.888888889 = 0.000000000
0.000000000 + -4x + x2 = 0 + 3.888888889
-4x + x2 = 0 + 3.888888889

Combine like terms: 0 + 3.888888889 = 3.888888889
-4x + x2 = 3.888888889

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3.888888889 + 4

Reorder the terms:
4 + -4x + x2 = 3.888888889 + 4

Combine like terms: 3.888888889 + 4 = 7.888888889
4 + -4x + x2 = 7.888888889

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.888888889

Calculate the square root of the right side: 2.808716591

Break this problem into two subproblems by setting 
(x + -2) equal to 2.808716591 and -2.808716591.

Subproblem 1

x + -2 = 2.808716591 Simplifying x + -2 = 2.808716591 Reorder the terms: -2 + x = 2.808716591 Solving -2 + x = 2.808716591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.808716591 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.808716591 + 2 x = 2.808716591 + 2 Combine like terms: 2.808716591 + 2 = 4.808716591 x = 4.808716591 Simplifying x = 4.808716591

Subproblem 2

x + -2 = -2.808716591 Simplifying x + -2 = -2.808716591 Reorder the terms: -2 + x = -2.808716591 Solving -2 + x = -2.808716591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.808716591 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.808716591 + 2 x = -2.808716591 + 2 Combine like terms: -2.808716591 + 2 = -0.808716591 x = -0.808716591 Simplifying x = -0.808716591

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.808716591, -0.808716591}

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