x^2+50x-576=0

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Solution for x^2+50x-576=0 equation:


Simplifying
x2 + 50x + -576 = 0

Reorder the terms:
-576 + 50x + x2 = 0

Solving
-576 + 50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '576' to each side of the equation.
-576 + 50x + 576 + x2 = 0 + 576

Reorder the terms:
-576 + 576 + 50x + x2 = 0 + 576

Combine like terms: -576 + 576 = 0
0 + 50x + x2 = 0 + 576
50x + x2 = 0 + 576

Combine like terms: 0 + 576 = 576
50x + x2 = 576

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 576 + 625

Reorder the terms:
625 + 50x + x2 = 576 + 625

Combine like terms: 576 + 625 = 1201
625 + 50x + x2 = 1201

Factor a perfect square on the left side:
(x + 25)(x + 25) = 1201

Calculate the square root of the right side: 34.655446902

Break this problem into two subproblems by setting 
(x + 25) equal to 34.655446902 and -34.655446902.

Subproblem 1

x + 25 = 34.655446902 Simplifying x + 25 = 34.655446902 Reorder the terms: 25 + x = 34.655446902 Solving 25 + x = 34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 34.655446902 + -25 Combine like terms: 25 + -25 = 0 0 + x = 34.655446902 + -25 x = 34.655446902 + -25 Combine like terms: 34.655446902 + -25 = 9.655446902 x = 9.655446902 Simplifying x = 9.655446902

Subproblem 2

x + 25 = -34.655446902 Simplifying x + 25 = -34.655446902 Reorder the terms: 25 + x = -34.655446902 Solving 25 + x = -34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -34.655446902 + -25 Combine like terms: 25 + -25 = 0 0 + x = -34.655446902 + -25 x = -34.655446902 + -25 Combine like terms: -34.655446902 + -25 = -59.655446902 x = -59.655446902 Simplifying x = -59.655446902

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.655446902, -59.655446902}

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