20x^2+61x+35=0

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Solution for 20x^2+61x+35=0 equation:


Simplifying
20x2 + 61x + 35 = 0

Reorder the terms:
35 + 61x + 20x2 = 0

Solving
35 + 61x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
1.75 + 3.05x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 3.05x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 3.05x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 3.05x + x2 = 0 + -1.75
3.05x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
3.05x + x2 = -1.75

The x term is 3.05x.  Take half its coefficient (1.525).
Square it (2.325625) and add it to both sides.

Add '2.325625' to each side of the equation.
3.05x + 2.325625 + x2 = -1.75 + 2.325625

Reorder the terms:
2.325625 + 3.05x + x2 = -1.75 + 2.325625

Combine like terms: -1.75 + 2.325625 = 0.575625
2.325625 + 3.05x + x2 = 0.575625

Factor a perfect square on the left side:
(x + 1.525)(x + 1.525) = 0.575625

Calculate the square root of the right side: 0.758699545

Break this problem into two subproblems by setting 
(x + 1.525) equal to 0.758699545 and -0.758699545.

Subproblem 1

x + 1.525 = 0.758699545 Simplifying x + 1.525 = 0.758699545 Reorder the terms: 1.525 + x = 0.758699545 Solving 1.525 + x = 0.758699545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.525' to each side of the equation. 1.525 + -1.525 + x = 0.758699545 + -1.525 Combine like terms: 1.525 + -1.525 = 0.000 0.000 + x = 0.758699545 + -1.525 x = 0.758699545 + -1.525 Combine like terms: 0.758699545 + -1.525 = -0.766300455 x = -0.766300455 Simplifying x = -0.766300455

Subproblem 2

x + 1.525 = -0.758699545 Simplifying x + 1.525 = -0.758699545 Reorder the terms: 1.525 + x = -0.758699545 Solving 1.525 + x = -0.758699545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.525' to each side of the equation. 1.525 + -1.525 + x = -0.758699545 + -1.525 Combine like terms: 1.525 + -1.525 = 0.000 0.000 + x = -0.758699545 + -1.525 x = -0.758699545 + -1.525 Combine like terms: -0.758699545 + -1.525 = -2.283699545 x = -2.283699545 Simplifying x = -2.283699545

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.766300455, -2.283699545}

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