10-16x-x^2=0

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Solution for 10-16x-x^2=0 equation:


Simplifying
10 + -16x + -1x2 = 0

Solving
10 + -16x + -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 + 16x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 16x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 16x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 16x + x2 = 0 + 10
16x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
16x + x2 = 10

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 10 + 64

Reorder the terms:
64 + 16x + x2 = 10 + 64

Combine like terms: 10 + 64 = 74
64 + 16x + x2 = 74

Factor a perfect square on the left side:
(x + 8)(x + 8) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + 8) equal to 8.602325267 and -8.602325267.

Subproblem 1

x + 8 = 8.602325267 Simplifying x + 8 = 8.602325267 Reorder the terms: 8 + x = 8.602325267 Solving 8 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.602325267 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.602325267 + -8 x = 8.602325267 + -8 Combine like terms: 8.602325267 + -8 = 0.602325267 x = 0.602325267 Simplifying x = 0.602325267

Subproblem 2

x + 8 = -8.602325267 Simplifying x + 8 = -8.602325267 Reorder the terms: 8 + x = -8.602325267 Solving 8 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.602325267 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.602325267 + -8 x = -8.602325267 + -8 Combine like terms: -8.602325267 + -8 = -16.602325267 x = -16.602325267 Simplifying x = -16.602325267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.602325267, -16.602325267}

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