2x^2+20x=3

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Solution for 2x^2+20x=3 equation:


Simplifying
2x2 + 20x = 3

Reorder the terms:
20x + 2x2 = 3

Solving
20x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 20x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 20x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + 10x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 10x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 10x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 10x + x2 = 0 + 1.5
10x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
10x + x2 = 1.5

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 1.5 + 25

Reorder the terms:
25 + 10x + x2 = 1.5 + 25

Combine like terms: 1.5 + 25 = 26.5
25 + 10x + x2 = 26.5

Factor a perfect square on the left side:
(x + 5)(x + 5) = 26.5

Calculate the square root of the right side: 5.14781507

Break this problem into two subproblems by setting 
(x + 5) equal to 5.14781507 and -5.14781507.

Subproblem 1

x + 5 = 5.14781507 Simplifying x + 5 = 5.14781507 Reorder the terms: 5 + x = 5.14781507 Solving 5 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.14781507 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.14781507 + -5 x = 5.14781507 + -5 Combine like terms: 5.14781507 + -5 = 0.14781507 x = 0.14781507 Simplifying x = 0.14781507

Subproblem 2

x + 5 = -5.14781507 Simplifying x + 5 = -5.14781507 Reorder the terms: 5 + x = -5.14781507 Solving 5 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.14781507 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.14781507 + -5 x = -5.14781507 + -5 Combine like terms: -5.14781507 + -5 = -10.14781507 x = -10.14781507 Simplifying x = -10.14781507

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.14781507, -10.14781507}

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