0=5x+26-x^2

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Solution for 0=5x+26-x^2 equation:


Simplifying
0 = 5x + 26 + -1x2

Reorder the terms:
0 = 26 + 5x + -1x2

Solving
0 = 26 + 5x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -26 = -26
-26 + -5x + x2 = 26 + 5x + -1x2 + -26 + -5x + x2

Reorder the terms:
-26 + -5x + x2 = 26 + -26 + 5x + -5x + -1x2 + x2

Combine like terms: 26 + -26 = 0
-26 + -5x + x2 = 0 + 5x + -5x + -1x2 + x2
-26 + -5x + x2 = 5x + -5x + -1x2 + x2

Combine like terms: 5x + -5x = 0
-26 + -5x + x2 = 0 + -1x2 + x2
-26 + -5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-26 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -5x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -5x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5x + x2 = 0 + 26
-5x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-5x + x2 = 26

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 = 26 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 26 + 6.25

Combine like terms: 26 + 6.25 = 32.25
6.25 + -5x + x2 = 32.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -2.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + -2.5 = 5.678908346 Simplifying x + -2.5 = 5.678908346 Reorder the terms: -2.5 + x = 5.678908346 Solving -2.5 + x = 5.678908346 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 = 5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.678908346 + 2.5 x = 5.678908346 + 2.5 Combine like terms: 5.678908346 + 2.5 = 8.178908346 x = 8.178908346 Simplifying x = 8.178908346

Subproblem 2

x + -2.5 = -5.678908346 Simplifying x + -2.5 = -5.678908346 Reorder the terms: -2.5 + x = -5.678908346 Solving -2.5 + x = -5.678908346 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 = -5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.678908346 + 2.5 x = -5.678908346 + 2.5 Combine like terms: -5.678908346 + 2.5 = -3.178908346 x = -3.178908346 Simplifying x = -3.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.178908346, -3.178908346}

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