x^2-5x=13

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


Simplifying
x2 + -5x = 13

Reorder the terms:
-5x + x2 = 13

Solving
-5x + x2 = 13

Solving for variable 'x'.

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

Combine like terms: 13 + -13 = 0
-13 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -5x + 13 + x2 = 0 + 13

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

Combine like terms: -13 + 13 = 0
0 + -5x + x2 = 0 + 13
-5x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-5x + x2 = 13

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 = 13 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 13 + 6.25

Combine like terms: 13 + 6.25 = 19.25
6.25 + -5x + x2 = 19.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.387482194 and -4.387482194.

Subproblem 1

x + -2.5 = 4.387482194 Simplifying x + -2.5 = 4.387482194 Reorder the terms: -2.5 + x = 4.387482194 Solving -2.5 + x = 4.387482194 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 = 4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.387482194 + 2.5 x = 4.387482194 + 2.5 Combine like terms: 4.387482194 + 2.5 = 6.887482194 x = 6.887482194 Simplifying x = 6.887482194

Subproblem 2

x + -2.5 = -4.387482194 Simplifying x + -2.5 = -4.387482194 Reorder the terms: -2.5 + x = -4.387482194 Solving -2.5 + x = -4.387482194 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 = -4.387482194 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.387482194 + 2.5 x = -4.387482194 + 2.5 Combine like terms: -4.387482194 + 2.5 = -1.887482194 x = -1.887482194 Simplifying x = -1.887482194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.887482194, -1.887482194}

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