-x^2+4x+13=0

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Solution for -x^2+4x+13=0 equation:


Simplifying
-1x2 + 4x + 13 = 0

Reorder the terms:
13 + 4x + -1x2 = 0

Solving
13 + 4x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13 + -4x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -4x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -4x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4x + x2 = 0 + 13
-4x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-4x + x2 = 13

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 = 13 + 4

Reorder the terms:
4 + -4x + x2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + -4x + x2 = 17

Factor a perfect square on the left side:
(x + -2)(x + -2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -2) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -2 = 4.123105626 Simplifying x + -2 = 4.123105626 Reorder the terms: -2 + x = 4.123105626 Solving -2 + x = 4.123105626 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 = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.123105626 + 2 x = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 x = 6.123105626 Simplifying x = 6.123105626

Subproblem 2

x + -2 = -4.123105626 Simplifying x + -2 = -4.123105626 Reorder the terms: -2 + x = -4.123105626 Solving -2 + x = -4.123105626 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 = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.123105626 + 2 x = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 x = -2.123105626 Simplifying x = -2.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.123105626, -2.123105626}

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