35x^2+9x=9

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Solution for 35x^2+9x=9 equation:


Simplifying
35x2 + 9x = 9

Reorder the terms:
9x + 35x2 = 9

Solving
9x + 35x2 = 9

Solving for variable 'x'.

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

Combine like terms: 9 + -9 = 0
-9 + 9x + 35x2 = 0

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

Divide each side by '35'.
-0.2571428571 + 0.2571428571x + x2 = 0

Move the constant term to the right:

Add '0.2571428571' to each side of the equation.
-0.2571428571 + 0.2571428571x + 0.2571428571 + x2 = 0 + 0.2571428571

Reorder the terms:
-0.2571428571 + 0.2571428571 + 0.2571428571x + x2 = 0 + 0.2571428571

Combine like terms: -0.2571428571 + 0.2571428571 = 0.0000000000
0.0000000000 + 0.2571428571x + x2 = 0 + 0.2571428571
0.2571428571x + x2 = 0 + 0.2571428571

Combine like terms: 0 + 0.2571428571 = 0.2571428571
0.2571428571x + x2 = 0.2571428571

The x term is 0.2571428571x.  Take half its coefficient (0.1285714286).
Square it (0.01653061225) and add it to both sides.

Add '0.01653061225' to each side of the equation.
0.2571428571x + 0.01653061225 + x2 = 0.2571428571 + 0.01653061225

Reorder the terms:
0.01653061225 + 0.2571428571x + x2 = 0.2571428571 + 0.01653061225

Combine like terms: 0.2571428571 + 0.01653061225 = 0.27367346935
0.01653061225 + 0.2571428571x + x2 = 0.27367346935

Factor a perfect square on the left side:
(x + 0.1285714286)(x + 0.1285714286) = 0.27367346935

Calculate the square root of the right side: 0.523138098

Break this problem into two subproblems by setting 
(x + 0.1285714286) equal to 0.523138098 and -0.523138098.

Subproblem 1

x + 0.1285714286 = 0.523138098 Simplifying x + 0.1285714286 = 0.523138098 Reorder the terms: 0.1285714286 + x = 0.523138098 Solving 0.1285714286 + x = 0.523138098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1285714286' to each side of the equation. 0.1285714286 + -0.1285714286 + x = 0.523138098 + -0.1285714286 Combine like terms: 0.1285714286 + -0.1285714286 = 0.0000000000 0.0000000000 + x = 0.523138098 + -0.1285714286 x = 0.523138098 + -0.1285714286 Combine like terms: 0.523138098 + -0.1285714286 = 0.3945666694 x = 0.3945666694 Simplifying x = 0.3945666694

Subproblem 2

x + 0.1285714286 = -0.523138098 Simplifying x + 0.1285714286 = -0.523138098 Reorder the terms: 0.1285714286 + x = -0.523138098 Solving 0.1285714286 + x = -0.523138098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1285714286' to each side of the equation. 0.1285714286 + -0.1285714286 + x = -0.523138098 + -0.1285714286 Combine like terms: 0.1285714286 + -0.1285714286 = 0.0000000000 0.0000000000 + x = -0.523138098 + -0.1285714286 x = -0.523138098 + -0.1285714286 Combine like terms: -0.523138098 + -0.1285714286 = -0.6517095266 x = -0.6517095266 Simplifying x = -0.6517095266

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3945666694, -0.6517095266}

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