-x^2+10x=14

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Solution for -x^2+10x=14 equation:


Simplifying
-1x2 + 10x = 14

Reorder the terms:
10x + -1x2 = 14

Solving
10x + -1x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 10x + -1x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 10x + -1x2 = 0

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

Divide each side by '-1'.
14 + -10x + x2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -10x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -10x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -10x + x2 = 0 + -14
-10x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-10x + x2 = -14

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 = -14 + 25

Reorder the terms:
25 + -10x + x2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + -10x + x2 = 11

Factor a perfect square on the left side:
(x + -5)(x + -5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -5) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -5 = 3.31662479 Simplifying x + -5 = 3.31662479 Reorder the terms: -5 + x = 3.31662479 Solving -5 + x = 3.31662479 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 = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.31662479 + 5 x = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 x = 8.31662479 Simplifying x = 8.31662479

Subproblem 2

x + -5 = -3.31662479 Simplifying x + -5 = -3.31662479 Reorder the terms: -5 + x = -3.31662479 Solving -5 + x = -3.31662479 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 = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.31662479 + 5 x = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 x = 1.68337521 Simplifying x = 1.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.31662479, 1.68337521}

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