-x^2+10x+12=0

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Solution for -x^2+10x+12=0 equation:


Simplifying
-1x2 + 10x + 12 = 0

Reorder the terms:
12 + 10x + -1x2 = 0

Solving
12 + 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'.
-12 + -10x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -10x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -10x + x2 = 0 + 12

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

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

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 = 12 + 25

Reorder the terms:
25 + -10x + x2 = 12 + 25

Combine like terms: 12 + 25 = 37
25 + -10x + x2 = 37

Factor a perfect square on the left side:
(x + -5)(x + -5) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -5) equal to 6.08276253 and -6.08276253.

Subproblem 1

x + -5 = 6.08276253 Simplifying x + -5 = 6.08276253 Reorder the terms: -5 + x = 6.08276253 Solving -5 + x = 6.08276253 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 = 6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.08276253 + 5 x = 6.08276253 + 5 Combine like terms: 6.08276253 + 5 = 11.08276253 x = 11.08276253 Simplifying x = 11.08276253

Subproblem 2

x + -5 = -6.08276253 Simplifying x + -5 = -6.08276253 Reorder the terms: -5 + x = -6.08276253 Solving -5 + x = -6.08276253 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 = -6.08276253 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.08276253 + 5 x = -6.08276253 + 5 Combine like terms: -6.08276253 + 5 = -1.08276253 x = -1.08276253 Simplifying x = -1.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.08276253, -1.08276253}

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