x^2+10x-4x-40+x^2+16x-63=

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Solution for x^2+10x-4x-40+x^2+16x-63= equation:


Simplifying
x2 + 10x + -4x + -40 + x2 + 16x + -63 = 0

Reorder the terms:
-40 + -63 + 10x + -4x + 16x + x2 + x2 = 0

Combine like terms: -40 + -63 = -103
-103 + 10x + -4x + 16x + x2 + x2 = 0

Combine like terms: 10x + -4x = 6x
-103 + 6x + 16x + x2 + x2 = 0

Combine like terms: 6x + 16x = 22x
-103 + 22x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-103 + 22x + 2x2 = 0

Solving
-103 + 22x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-51.5 + 11x + x2 = 0

Move the constant term to the right:

Add '51.5' to each side of the equation.
-51.5 + 11x + 51.5 + x2 = 0 + 51.5

Reorder the terms:
-51.5 + 51.5 + 11x + x2 = 0 + 51.5

Combine like terms: -51.5 + 51.5 = 0.0
0.0 + 11x + x2 = 0 + 51.5
11x + x2 = 0 + 51.5

Combine like terms: 0 + 51.5 = 51.5
11x + x2 = 51.5

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 51.5 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 51.5 + 30.25

Combine like terms: 51.5 + 30.25 = 81.75
30.25 + 11x + x2 = 81.75

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 81.75

Calculate the square root of the right side: 9.04157066

Break this problem into two subproblems by setting 
(x + 5.5) equal to 9.04157066 and -9.04157066.

Subproblem 1

x + 5.5 = 9.04157066 Simplifying x + 5.5 = 9.04157066 Reorder the terms: 5.5 + x = 9.04157066 Solving 5.5 + x = 9.04157066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.04157066 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.04157066 + -5.5 x = 9.04157066 + -5.5 Combine like terms: 9.04157066 + -5.5 = 3.54157066 x = 3.54157066 Simplifying x = 3.54157066

Subproblem 2

x + 5.5 = -9.04157066 Simplifying x + 5.5 = -9.04157066 Reorder the terms: 5.5 + x = -9.04157066 Solving 5.5 + x = -9.04157066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.04157066 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.04157066 + -5.5 x = -9.04157066 + -5.5 Combine like terms: -9.04157066 + -5.5 = -14.54157066 x = -14.54157066 Simplifying x = -14.54157066

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.54157066, -14.54157066}

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