13x^2-65x-1050=0

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Solution for 13x^2-65x-1050=0 equation:


Simplifying
13x2 + -65x + -1050 = 0

Reorder the terms:
-1050 + -65x + 13x2 = 0

Solving
-1050 + -65x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-80.76923077 + -5x + x2 = 0

Move the constant term to the right:

Add '80.76923077' to each side of the equation.
-80.76923077 + -5x + 80.76923077 + x2 = 0 + 80.76923077

Reorder the terms:
-80.76923077 + 80.76923077 + -5x + x2 = 0 + 80.76923077

Combine like terms: -80.76923077 + 80.76923077 = 0.00000000
0.00000000 + -5x + x2 = 0 + 80.76923077
-5x + x2 = 0 + 80.76923077

Combine like terms: 0 + 80.76923077 = 80.76923077
-5x + x2 = 80.76923077

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 80.76923077 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 80.76923077 + 6.25

Combine like terms: 80.76923077 + 6.25 = 87.01923077
6.25 + -5x + x2 = 87.01923077

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 87.01923077

Calculate the square root of the right side: 9.328409874

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.328409874 and -9.328409874.

Subproblem 1

x + -2.5 = 9.328409874 Simplifying x + -2.5 = 9.328409874 Reorder the terms: -2.5 + x = 9.328409874 Solving -2.5 + x = 9.328409874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.328409874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.328409874 + 2.5 x = 9.328409874 + 2.5 Combine like terms: 9.328409874 + 2.5 = 11.828409874 x = 11.828409874 Simplifying x = 11.828409874

Subproblem 2

x + -2.5 = -9.328409874 Simplifying x + -2.5 = -9.328409874 Reorder the terms: -2.5 + x = -9.328409874 Solving -2.5 + x = -9.328409874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.328409874 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.328409874 + 2.5 x = -9.328409874 + 2.5 Combine like terms: -9.328409874 + 2.5 = -6.828409874 x = -6.828409874 Simplifying x = -6.828409874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.828409874, -6.828409874}

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