5x^2+5-13x=0

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


Simplifying
5x2 + 5 + -13x = 0

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

Solving
5 + -13x + 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'.
1 + -2.6x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.6x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.6x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.6x + x2 = 0 + -1
-2.6x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.6x + x2 = -1

The x term is -2.6x.  Take half its coefficient (-1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
-2.6x + 1.69 + x2 = -1 + 1.69

Reorder the terms:
1.69 + -2.6x + x2 = -1 + 1.69

Combine like terms: -1 + 1.69 = 0.69
1.69 + -2.6x + x2 = 0.69

Factor a perfect square on the left side:
(x + -1.3)(x + -1.3) = 0.69

Calculate the square root of the right side: 0.830662386

Break this problem into two subproblems by setting 
(x + -1.3) equal to 0.830662386 and -0.830662386.

Subproblem 1

x + -1.3 = 0.830662386 Simplifying x + -1.3 = 0.830662386 Reorder the terms: -1.3 + x = 0.830662386 Solving -1.3 + x = 0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 0.830662386 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 0.830662386 + 1.3 x = 0.830662386 + 1.3 Combine like terms: 0.830662386 + 1.3 = 2.130662386 x = 2.130662386 Simplifying x = 2.130662386

Subproblem 2

x + -1.3 = -0.830662386 Simplifying x + -1.3 = -0.830662386 Reorder the terms: -1.3 + x = -0.830662386 Solving -1.3 + x = -0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -0.830662386 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -0.830662386 + 1.3 x = -0.830662386 + 1.3 Combine like terms: -0.830662386 + 1.3 = 0.469337614 x = 0.469337614 Simplifying x = 0.469337614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.130662386, 0.469337614}

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