-x^2+60x+550=0

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Solution for -x^2+60x+550=0 equation:


Simplifying
-1x2 + 60x + 550 = 0

Reorder the terms:
550 + 60x + -1x2 = 0

Solving
550 + 60x + -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'.
-550 + -60x + x2 = 0

Move the constant term to the right:

Add '550' to each side of the equation.
-550 + -60x + 550 + x2 = 0 + 550

Reorder the terms:
-550 + 550 + -60x + x2 = 0 + 550

Combine like terms: -550 + 550 = 0
0 + -60x + x2 = 0 + 550
-60x + x2 = 0 + 550

Combine like terms: 0 + 550 = 550
-60x + x2 = 550

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = 550 + 900

Reorder the terms:
900 + -60x + x2 = 550 + 900

Combine like terms: 550 + 900 = 1450
900 + -60x + x2 = 1450

Factor a perfect square on the left side:
(x + -30)(x + -30) = 1450

Calculate the square root of the right side: 38.078865529

Break this problem into two subproblems by setting 
(x + -30) equal to 38.078865529 and -38.078865529.

Subproblem 1

x + -30 = 38.078865529 Simplifying x + -30 = 38.078865529 Reorder the terms: -30 + x = 38.078865529 Solving -30 + x = 38.078865529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 38.078865529 + 30 Combine like terms: -30 + 30 = 0 0 + x = 38.078865529 + 30 x = 38.078865529 + 30 Combine like terms: 38.078865529 + 30 = 68.078865529 x = 68.078865529 Simplifying x = 68.078865529

Subproblem 2

x + -30 = -38.078865529 Simplifying x + -30 = -38.078865529 Reorder the terms: -30 + x = -38.078865529 Solving -30 + x = -38.078865529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -38.078865529 + 30 Combine like terms: -30 + 30 = 0 0 + x = -38.078865529 + 30 x = -38.078865529 + 30 Combine like terms: -38.078865529 + 30 = -8.078865529 x = -8.078865529 Simplifying x = -8.078865529

Solution

The solution to the problem is based on the solutions from the subproblems. x = {68.078865529, -8.078865529}

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