0=-5x^2-20x+3

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Solution for 0=-5x^2-20x+3 equation:


Simplifying
0 = -5x2 + -20x + 3

Reorder the terms:
0 = 3 + -20x + -5x2

Solving
0 = 3 + -20x + -5x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + 20x + 5x2 = 3 + -20x + -5x2 + -3 + 20x + 5x2

Reorder the terms:
-3 + 20x + 5x2 = 3 + -3 + -20x + 20x + -5x2 + 5x2

Combine like terms: 3 + -3 = 0
-3 + 20x + 5x2 = 0 + -20x + 20x + -5x2 + 5x2
-3 + 20x + 5x2 = -20x + 20x + -5x2 + 5x2

Combine like terms: -20x + 20x = 0
-3 + 20x + 5x2 = 0 + -5x2 + 5x2
-3 + 20x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-3 + 20x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 4x + x2 = 0 + 0.6
4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
4x + x2 = 0.6

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 = 0.6 + 4

Reorder the terms:
4 + 4x + x2 = 0.6 + 4

Combine like terms: 0.6 + 4 = 4.6
4 + 4x + x2 = 4.6

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.6

Calculate the square root of the right side: 2.144761059

Break this problem into two subproblems by setting 
(x + 2) equal to 2.144761059 and -2.144761059.

Subproblem 1

x + 2 = 2.144761059 Simplifying x + 2 = 2.144761059 Reorder the terms: 2 + x = 2.144761059 Solving 2 + x = 2.144761059 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 = 2.144761059 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.144761059 + -2 x = 2.144761059 + -2 Combine like terms: 2.144761059 + -2 = 0.144761059 x = 0.144761059 Simplifying x = 0.144761059

Subproblem 2

x + 2 = -2.144761059 Simplifying x + 2 = -2.144761059 Reorder the terms: 2 + x = -2.144761059 Solving 2 + x = -2.144761059 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 = -2.144761059 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.144761059 + -2 x = -2.144761059 + -2 Combine like terms: -2.144761059 + -2 = -4.144761059 x = -4.144761059 Simplifying x = -4.144761059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.144761059, -4.144761059}

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