8+10x-x^2=0

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Solution for 8+10x-x^2=0 equation:


Simplifying
8 + 10x + -1x2 = 0

Solving
8 + 10x + -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'.
-8 + -10x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -10x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -10x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -10x + x2 = 0 + 8
-10x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-10x + x2 = 8

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 8 + 25

Reorder the terms:
25 + -10x + x2 = 8 + 25

Combine like terms: 8 + 25 = 33
25 + -10x + x2 = 33

Factor a perfect square on the left side:
(x + -5)(x + -5) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -5) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -5 = 5.744562647 Simplifying x + -5 = 5.744562647 Reorder the terms: -5 + x = 5.744562647 Solving -5 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.744562647 + 5 x = 5.744562647 + 5 Combine like terms: 5.744562647 + 5 = 10.744562647 x = 10.744562647 Simplifying x = 10.744562647

Subproblem 2

x + -5 = -5.744562647 Simplifying x + -5 = -5.744562647 Reorder the terms: -5 + x = -5.744562647 Solving -5 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.744562647 + 5 x = -5.744562647 + 5 Combine like terms: -5.744562647 + 5 = -0.744562647 x = -0.744562647 Simplifying x = -0.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.744562647, -0.744562647}

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