-x^2-25x+30=0

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Solution for -x^2-25x+30=0 equation:


Simplifying
-1x2 + -25x + 30 = 0

Reorder the terms:
30 + -25x + -1x2 = 0

Solving
30 + -25x + -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'.
-30 + 25x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 25x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 25x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 25x + x2 = 0 + 30
25x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
25x + x2 = 30

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 30 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 30 + 156.25

Combine like terms: 30 + 156.25 = 186.25
156.25 + 25x + x2 = 186.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 186.25

Calculate the square root of the right side: 13.647344064

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.647344064 and -13.647344064.

Subproblem 1

x + 12.5 = 13.647344064 Simplifying x + 12.5 = 13.647344064 Reorder the terms: 12.5 + x = 13.647344064 Solving 12.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 13.647344064 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.647344064 + -12.5 x = 13.647344064 + -12.5 Combine like terms: 13.647344064 + -12.5 = 1.147344064 x = 1.147344064 Simplifying x = 1.147344064

Subproblem 2

x + 12.5 = -13.647344064 Simplifying x + 12.5 = -13.647344064 Reorder the terms: 12.5 + x = -13.647344064 Solving 12.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -13.647344064 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.647344064 + -12.5 x = -13.647344064 + -12.5 Combine like terms: -13.647344064 + -12.5 = -26.147344064 x = -26.147344064 Simplifying x = -26.147344064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.147344064, -26.147344064}

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