5x^2-17x+7.35=0

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Solution for 5x^2-17x+7.35=0 equation:


Simplifying
5x2 + -17x + 7.35 = 0

Reorder the terms:
7.35 + -17x + 5x2 = 0

Solving
7.35 + -17x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.47 + -3.4x + x2 = 0

Move the constant term to the right:

Add '-1.47' to each side of the equation.
1.47 + -3.4x + -1.47 + x2 = 0 + -1.47

Reorder the terms:
1.47 + -1.47 + -3.4x + x2 = 0 + -1.47

Combine like terms: 1.47 + -1.47 = 0.00
0.00 + -3.4x + x2 = 0 + -1.47
-3.4x + x2 = 0 + -1.47

Combine like terms: 0 + -1.47 = -1.47
-3.4x + x2 = -1.47

The x term is -3.4x.  Take half its coefficient (-1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
-3.4x + 2.89 + x2 = -1.47 + 2.89

Reorder the terms:
2.89 + -3.4x + x2 = -1.47 + 2.89

Combine like terms: -1.47 + 2.89 = 1.42
2.89 + -3.4x + x2 = 1.42

Factor a perfect square on the left side:
(x + -1.7)(x + -1.7) = 1.42

Calculate the square root of the right side: 1.191637529

Break this problem into two subproblems by setting 
(x + -1.7) equal to 1.191637529 and -1.191637529.

Subproblem 1

x + -1.7 = 1.191637529 Simplifying x + -1.7 = 1.191637529 Reorder the terms: -1.7 + x = 1.191637529 Solving -1.7 + x = 1.191637529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 1.191637529 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.191637529 + 1.7 x = 1.191637529 + 1.7 Combine like terms: 1.191637529 + 1.7 = 2.891637529 x = 2.891637529 Simplifying x = 2.891637529

Subproblem 2

x + -1.7 = -1.191637529 Simplifying x + -1.7 = -1.191637529 Reorder the terms: -1.7 + x = -1.191637529 Solving -1.7 + x = -1.191637529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -1.191637529 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.191637529 + 1.7 x = -1.191637529 + 1.7 Combine like terms: -1.191637529 + 1.7 = 0.508362471 x = 0.508362471 Simplifying x = 0.508362471

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.891637529, 0.508362471}

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