0=2x^2-47x+35

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Solution for 0=2x^2-47x+35 equation:


Simplifying
0 = 2x2 + -47x + 35

Reorder the terms:
0 = 35 + -47x + 2x2

Solving
0 = 35 + -47x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -35 = -35
-35 + 47x + -2x2 = 35 + -47x + 2x2 + -35 + 47x + -2x2

Reorder the terms:
-35 + 47x + -2x2 = 35 + -35 + -47x + 47x + 2x2 + -2x2

Combine like terms: 35 + -35 = 0
-35 + 47x + -2x2 = 0 + -47x + 47x + 2x2 + -2x2
-35 + 47x + -2x2 = -47x + 47x + 2x2 + -2x2

Combine like terms: -47x + 47x = 0
-35 + 47x + -2x2 = 0 + 2x2 + -2x2
-35 + 47x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-35 + 47x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
17.5 + -23.5x + x2 = 0

Move the constant term to the right:

Add '-17.5' to each side of the equation.
17.5 + -23.5x + -17.5 + x2 = 0 + -17.5

Reorder the terms:
17.5 + -17.5 + -23.5x + x2 = 0 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + -23.5x + x2 = 0 + -17.5
-23.5x + x2 = 0 + -17.5

Combine like terms: 0 + -17.5 = -17.5
-23.5x + x2 = -17.5

The x term is -23.5x.  Take half its coefficient (-11.75).
Square it (138.0625) and add it to both sides.

Add '138.0625' to each side of the equation.
-23.5x + 138.0625 + x2 = -17.5 + 138.0625

Reorder the terms:
138.0625 + -23.5x + x2 = -17.5 + 138.0625

Combine like terms: -17.5 + 138.0625 = 120.5625
138.0625 + -23.5x + x2 = 120.5625

Factor a perfect square on the left side:
(x + -11.75)(x + -11.75) = 120.5625

Calculate the square root of the right side: 10.980095628

Break this problem into two subproblems by setting 
(x + -11.75) equal to 10.980095628 and -10.980095628.

Subproblem 1

x + -11.75 = 10.980095628 Simplifying x + -11.75 = 10.980095628 Reorder the terms: -11.75 + x = 10.980095628 Solving -11.75 + x = 10.980095628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 10.980095628 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 10.980095628 + 11.75 x = 10.980095628 + 11.75 Combine like terms: 10.980095628 + 11.75 = 22.730095628 x = 22.730095628 Simplifying x = 22.730095628

Subproblem 2

x + -11.75 = -10.980095628 Simplifying x + -11.75 = -10.980095628 Reorder the terms: -11.75 + x = -10.980095628 Solving -11.75 + x = -10.980095628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -10.980095628 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -10.980095628 + 11.75 x = -10.980095628 + 11.75 Combine like terms: -10.980095628 + 11.75 = 0.769904372 x = 0.769904372 Simplifying x = 0.769904372

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.730095628, 0.769904372}

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