9x^2-35x+18=0

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Solution for 9x^2-35x+18=0 equation:


Simplifying
9x2 + -35x + 18 = 0

Reorder the terms:
18 + -35x + 9x2 = 0

Solving
18 + -35x + 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'.
2 + -3.888888889x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.888888889x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.888888889x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.888888889x + x2 = 0 + -2
-3.888888889x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.888888889x + x2 = -2

The x term is -3.888888889x.  Take half its coefficient (-1.944444445).
Square it (3.780864200) and add it to both sides.

Add '3.780864200' to each side of the equation.
-3.888888889x + 3.780864200 + x2 = -2 + 3.780864200

Reorder the terms:
3.780864200 + -3.888888889x + x2 = -2 + 3.780864200

Combine like terms: -2 + 3.780864200 = 1.7808642
3.780864200 + -3.888888889x + x2 = 1.7808642

Factor a perfect square on the left side:
(x + -1.944444445)(x + -1.944444445) = 1.7808642

Calculate the square root of the right side: 1.33449024

Break this problem into two subproblems by setting 
(x + -1.944444445) equal to 1.33449024 and -1.33449024.

Subproblem 1

x + -1.944444445 = 1.33449024 Simplifying x + -1.944444445 = 1.33449024 Reorder the terms: -1.944444445 + x = 1.33449024 Solving -1.944444445 + x = 1.33449024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = 1.33449024 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = 1.33449024 + 1.944444445 x = 1.33449024 + 1.944444445 Combine like terms: 1.33449024 + 1.944444445 = 3.278934685 x = 3.278934685 Simplifying x = 3.278934685

Subproblem 2

x + -1.944444445 = -1.33449024 Simplifying x + -1.944444445 = -1.33449024 Reorder the terms: -1.944444445 + x = -1.33449024 Solving -1.944444445 + x = -1.33449024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.944444445' to each side of the equation. -1.944444445 + 1.944444445 + x = -1.33449024 + 1.944444445 Combine like terms: -1.944444445 + 1.944444445 = 0.000000000 0.000000000 + x = -1.33449024 + 1.944444445 x = -1.33449024 + 1.944444445 Combine like terms: -1.33449024 + 1.944444445 = 0.609954205 x = 0.609954205 Simplifying x = 0.609954205

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.278934685, 0.609954205}

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