-5x^2+20x-13=0

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Solution for -5x^2+20x-13=0 equation:


Simplifying
-5x2 + 20x + -13 = 0

Reorder the terms:
-13 + 20x + -5x2 = 0

Solving
-13 + 20x + -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'.
2.6 + -4x + x2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + -4x + -2.6 + x2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + -4x + x2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + -4x + x2 = 0 + -2.6
-4x + x2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
-4x + x2 = -2.6

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 = -2.6 + 4

Reorder the terms:
4 + -4x + x2 = -2.6 + 4

Combine like terms: -2.6 + 4 = 1.4
4 + -4x + x2 = 1.4

Factor a perfect square on the left side:
(x + -2)(x + -2) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(x + -2) equal to 1.183215957 and -1.183215957.

Subproblem 1

x + -2 = 1.183215957 Simplifying x + -2 = 1.183215957 Reorder the terms: -2 + x = 1.183215957 Solving -2 + x = 1.183215957 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 = 1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.183215957 + 2 x = 1.183215957 + 2 Combine like terms: 1.183215957 + 2 = 3.183215957 x = 3.183215957 Simplifying x = 3.183215957

Subproblem 2

x + -2 = -1.183215957 Simplifying x + -2 = -1.183215957 Reorder the terms: -2 + x = -1.183215957 Solving -2 + x = -1.183215957 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 = -1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.183215957 + 2 x = -1.183215957 + 2 Combine like terms: -1.183215957 + 2 = 0.816784043 x = 0.816784043 Simplifying x = 0.816784043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.183215957, 0.816784043}

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