-x^2+10x+4=12

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Solution for -x^2+10x+4=12 equation:


Simplifying
-1x2 + 10x + 4 = 12

Reorder the terms:
4 + 10x + -1x2 = 12

Solving
4 + 10x + -1x2 = 12

Solving for variable 'x'.

Reorder the terms:
4 + -12 + 10x + -1x2 = 12 + -12

Combine like terms: 4 + -12 = -8
-8 + 10x + -1x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-8 + 10x + -1x2 = 0

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 = 17
25 + -10x + x2 = 17

Factor a perfect square on the left side:
(x + -5)(x + -5) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -5) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -5 = 4.123105626 Simplifying x + -5 = 4.123105626 Reorder the terms: -5 + x = 4.123105626 Solving -5 + x = 4.123105626 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 = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.123105626 + 5 x = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 x = 9.123105626 Simplifying x = 9.123105626

Subproblem 2

x + -5 = -4.123105626 Simplifying x + -5 = -4.123105626 Reorder the terms: -5 + x = -4.123105626 Solving -5 + x = -4.123105626 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 = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.123105626 + 5 x = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 x = 0.876894374 Simplifying x = 0.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.123105626, 0.876894374}

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