-x^2+8x=5

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Solution for -x^2+8x=5 equation:


Simplifying
-1x2 + 8x = 5

Reorder the terms:
8x + -1x2 = 5

Solving
8x + -1x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 8x + -1x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 8x + -1x2 = 0

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

Divide each side by '-1'.
5 + -8x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x + x2 = 0 + -5
-8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x + x2 = -5

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 = -5 + 16

Reorder the terms:
16 + -8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x + x2 = 11

Factor a perfect square on the left side:
(x + -4)(x + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479

Subproblem 2

x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}

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