0=5x^2+20x-6

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Solution for 0=5x^2+20x-6 equation:


Simplifying
0 = 5x2 + 20x + -6

Reorder the terms:
0 = -6 + 20x + 5x2

Solving
0 = -6 + 20x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + -20x + -5x2 = -6 + 20x + 5x2 + 6 + -20x + -5x2

Reorder the terms:
6 + -20x + -5x2 = -6 + 6 + 20x + -20x + 5x2 + -5x2

Combine like terms: -6 + 6 = 0
6 + -20x + -5x2 = 0 + 20x + -20x + 5x2 + -5x2
6 + -20x + -5x2 = 20x + -20x + 5x2 + -5x2

Combine like terms: 20x + -20x = 0
6 + -20x + -5x2 = 0 + 5x2 + -5x2
6 + -20x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
6 + -20x + -5x2 = 0

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

Divide each side by '-5'.
-1.2 + 4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 4x + x2 = 0 + 1.2
4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
4x + x2 = 1.2

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.2 + 4

Reorder the terms:
4 + 4x + x2 = 1.2 + 4

Combine like terms: 1.2 + 4 = 5.2
4 + 4x + x2 = 5.2

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.2

Calculate the square root of the right side: 2.28035085

Break this problem into two subproblems by setting 
(x + 2) equal to 2.28035085 and -2.28035085.

Subproblem 1

x + 2 = 2.28035085 Simplifying x + 2 = 2.28035085 Reorder the terms: 2 + x = 2.28035085 Solving 2 + x = 2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.28035085 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.28035085 + -2 x = 2.28035085 + -2 Combine like terms: 2.28035085 + -2 = 0.28035085 x = 0.28035085 Simplifying x = 0.28035085

Subproblem 2

x + 2 = -2.28035085 Simplifying x + 2 = -2.28035085 Reorder the terms: 2 + x = -2.28035085 Solving 2 + x = -2.28035085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.28035085 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.28035085 + -2 x = -2.28035085 + -2 Combine like terms: -2.28035085 + -2 = -4.28035085 x = -4.28035085 Simplifying x = -4.28035085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.28035085, -4.28035085}

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