x^2+10x+0=576

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Solution for x^2+10x+0=576 equation:


Simplifying
x2 + 10x + 0 = 576

Reorder the terms:
0 + 10x + x2 = 576
Remove the zero:
10x + x2 = 576

Solving
10x + x2 = 576

Solving for variable 'x'.

Reorder the terms:
-576 + 10x + x2 = 576 + -576

Combine like terms: 576 + -576 = 0
-576 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + 10x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + 10x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + 10x + x2 = 0 + 576
10x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
10x + x2 = 576

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 = 576 + 25

Reorder the terms:
25 + 10x + x2 = 576 + 25

Combine like terms: 576 + 25 = 601
25 + 10x + x2 = 601

Factor a perfect square on the left side:
(x + 5)(x + 5) = 601

Calculate the square root of the right side: 24.515301344

Break this problem into two subproblems by setting 
(x + 5) equal to 24.515301344 and -24.515301344.

Subproblem 1

x + 5 = 24.515301344 Simplifying x + 5 = 24.515301344 Reorder the terms: 5 + x = 24.515301344 Solving 5 + x = 24.515301344 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 = 24.515301344 + -5 Combine like terms: 5 + -5 = 0 0 + x = 24.515301344 + -5 x = 24.515301344 + -5 Combine like terms: 24.515301344 + -5 = 19.515301344 x = 19.515301344 Simplifying x = 19.515301344

Subproblem 2

x + 5 = -24.515301344 Simplifying x + 5 = -24.515301344 Reorder the terms: 5 + x = -24.515301344 Solving 5 + x = -24.515301344 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 = -24.515301344 + -5 Combine like terms: 5 + -5 = 0 0 + x = -24.515301344 + -5 x = -24.515301344 + -5 Combine like terms: -24.515301344 + -5 = -29.515301344 x = -29.515301344 Simplifying x = -29.515301344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.515301344, -29.515301344}

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