9x^2=3-5x

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Solution for 9x^2=3-5x equation:


Simplifying
9x2 = 3 + -5x

Solving
9x2 = 3 + -5x

Solving for variable 'x'.

Reorder the terms:
-3 + 5x + 9x2 = 3 + -5x + -3 + 5x

Reorder the terms:
-3 + 5x + 9x2 = 3 + -3 + -5x + 5x

Combine like terms: 3 + -3 = 0
-3 + 5x + 9x2 = 0 + -5x + 5x
-3 + 5x + 9x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-3 + 5x + 9x2 = 0

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

Divide each side by '9'.
-0.3333333333 + 0.5555555556x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5555555556x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5555555556x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5555555556x + x2 = 0 + 0.3333333333
0.5555555556x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5555555556x + x2 = 0.3333333333

The x term is 0.5555555556x.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556x + 0.07716049384 + x2 = 0.3333333333 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556x + x2 = 0.3333333333 + 0.07716049384

Combine like terms: 0.3333333333 + 0.07716049384 = 0.41049382714
0.07716049384 + 0.5555555556x + x2 = 0.41049382714

Factor a perfect square on the left side:
(x + 0.2777777778)(x + 0.2777777778) = 0.41049382714

Calculate the square root of the right side: 0.640697922

Break this problem into two subproblems by setting 
(x + 0.2777777778) equal to 0.640697922 and -0.640697922.

Subproblem 1

x + 0.2777777778 = 0.640697922 Simplifying x + 0.2777777778 = 0.640697922 Reorder the terms: 0.2777777778 + x = 0.640697922 Solving 0.2777777778 + x = 0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.640697922 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.640697922 + -0.2777777778 x = 0.640697922 + -0.2777777778 Combine like terms: 0.640697922 + -0.2777777778 = 0.3629201442 x = 0.3629201442 Simplifying x = 0.3629201442

Subproblem 2

x + 0.2777777778 = -0.640697922 Simplifying x + 0.2777777778 = -0.640697922 Reorder the terms: 0.2777777778 + x = -0.640697922 Solving 0.2777777778 + x = -0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.640697922 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.640697922 + -0.2777777778 x = -0.640697922 + -0.2777777778 Combine like terms: -0.640697922 + -0.2777777778 = -0.9184756998 x = -0.9184756998 Simplifying x = -0.9184756998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3629201442, -0.9184756998}

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