10-x^2+8x=0

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


Simplifying
10 + -1x2 + 8x = 0

Reorder the terms:
10 + 8x + -1x2 = 0

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

Move the constant term to the right:

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

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

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 10 + 16

Reorder the terms:
16 + -8x + x2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + -8x + x2 = 26

Factor a perfect square on the left side:
(x + -4)(x + -4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -4) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + -4 = 5.099019514 Simplifying x + -4 = 5.099019514 Reorder the terms: -4 + x = 5.099019514 Solving -4 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.099019514 + 4 x = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 x = 9.099019514 Simplifying x = 9.099019514

Subproblem 2

x + -4 = -5.099019514 Simplifying x + -4 = -5.099019514 Reorder the terms: -4 + x = -5.099019514 Solving -4 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.099019514 + 4 x = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 x = -1.099019514 Simplifying x = -1.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.099019514, -1.099019514}

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