9x^2-77x+4=0

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Solution for 9x^2-77x+4=0 equation:


Simplifying
9x2 + -77x + 4 = 0

Reorder the terms:
4 + -77x + 9x2 = 0

Solving
4 + -77x + 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'.
0.4444444444 + -8.555555556x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -8.555555556x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -8.555555556x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -8.555555556x + x2 = 0 + -0.4444444444
-8.555555556x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-8.555555556x + x2 = -0.4444444444

The x term is -8.555555556x.  Take half its coefficient (-4.277777778).
Square it (18.29938272) and add it to both sides.

Add '18.29938272' to each side of the equation.
-8.555555556x + 18.29938272 + x2 = -0.4444444444 + 18.29938272

Reorder the terms:
18.29938272 + -8.555555556x + x2 = -0.4444444444 + 18.29938272

Combine like terms: -0.4444444444 + 18.29938272 = 17.8549382756
18.29938272 + -8.555555556x + x2 = 17.8549382756

Factor a perfect square on the left side:
(x + -4.277777778)(x + -4.277777778) = 17.8549382756

Calculate the square root of the right side: 4.225510416

Break this problem into two subproblems by setting 
(x + -4.277777778) equal to 4.225510416 and -4.225510416.

Subproblem 1

x + -4.277777778 = 4.225510416 Simplifying x + -4.277777778 = 4.225510416 Reorder the terms: -4.277777778 + x = 4.225510416 Solving -4.277777778 + x = 4.225510416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = 4.225510416 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = 4.225510416 + 4.277777778 x = 4.225510416 + 4.277777778 Combine like terms: 4.225510416 + 4.277777778 = 8.503288194 x = 8.503288194 Simplifying x = 8.503288194

Subproblem 2

x + -4.277777778 = -4.225510416 Simplifying x + -4.277777778 = -4.225510416 Reorder the terms: -4.277777778 + x = -4.225510416 Solving -4.277777778 + x = -4.225510416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = -4.225510416 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = -4.225510416 + 4.277777778 x = -4.225510416 + 4.277777778 Combine like terms: -4.225510416 + 4.277777778 = 0.052267362 x = 0.052267362 Simplifying x = 0.052267362

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.503288194, 0.052267362}

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