9x^2-40x+40=0

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Solution for 9x^2-40x+40=0 equation:


Simplifying
9x2 + -40x + 40 = 0

Reorder the terms:
40 + -40x + 9x2 = 0

Solving
40 + -40x + 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'.
4.444444444 + -4.444444444x + x2 = 0

Move the constant term to the right:

Add '-4.444444444' to each side of the equation.
4.444444444 + -4.444444444x + -4.444444444 + x2 = 0 + -4.444444444

Reorder the terms:
4.444444444 + -4.444444444 + -4.444444444x + x2 = 0 + -4.444444444

Combine like terms: 4.444444444 + -4.444444444 = 0.000000000
0.000000000 + -4.444444444x + x2 = 0 + -4.444444444
-4.444444444x + x2 = 0 + -4.444444444

Combine like terms: 0 + -4.444444444 = -4.444444444
-4.444444444x + x2 = -4.444444444

The x term is -4.444444444x.  Take half its coefficient (-2.222222222).
Square it (4.938271604) and add it to both sides.

Add '4.938271604' to each side of the equation.
-4.444444444x + 4.938271604 + x2 = -4.444444444 + 4.938271604

Reorder the terms:
4.938271604 + -4.444444444x + x2 = -4.444444444 + 4.938271604

Combine like terms: -4.444444444 + 4.938271604 = 0.49382716
4.938271604 + -4.444444444x + x2 = 0.49382716

Factor a perfect square on the left side:
(x + -2.222222222)(x + -2.222222222) = 0.49382716

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(x + -2.222222222) equal to 0.702728369 and -0.702728369.

Subproblem 1

x + -2.222222222 = 0.702728369 Simplifying x + -2.222222222 = 0.702728369 Reorder the terms: -2.222222222 + x = 0.702728369 Solving -2.222222222 + x = 0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 0.702728369 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 0.702728369 + 2.222222222 x = 0.702728369 + 2.222222222 Combine like terms: 0.702728369 + 2.222222222 = 2.924950591 x = 2.924950591 Simplifying x = 2.924950591

Subproblem 2

x + -2.222222222 = -0.702728369 Simplifying x + -2.222222222 = -0.702728369 Reorder the terms: -2.222222222 + x = -0.702728369 Solving -2.222222222 + x = -0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -0.702728369 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -0.702728369 + 2.222222222 x = -0.702728369 + 2.222222222 Combine like terms: -0.702728369 + 2.222222222 = 1.519493853 x = 1.519493853 Simplifying x = 1.519493853

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.924950591, 1.519493853}

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