x^2+25x-24=0

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Solution for x^2+25x-24=0 equation:


Simplifying
x2 + 25x + -24 = 0

Reorder the terms:
-24 + 25x + x2 = 0

Solving
-24 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 25x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 25x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 25x + x2 = 0 + 24
25x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
25x + x2 = 24

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 = 24 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 24 + 156.25

Combine like terms: 24 + 156.25 = 180.25
156.25 + 25x + x2 = 180.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.425721582 and -13.425721582.

Subproblem 1

x + 12.5 = 13.425721582 Simplifying x + 12.5 = 13.425721582 Reorder the terms: 12.5 + x = 13.425721582 Solving 12.5 + x = 13.425721582 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 = 13.425721582 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.425721582 + -12.5 x = 13.425721582 + -12.5 Combine like terms: 13.425721582 + -12.5 = 0.925721582 x = 0.925721582 Simplifying x = 0.925721582

Subproblem 2

x + 12.5 = -13.425721582 Simplifying x + 12.5 = -13.425721582 Reorder the terms: 12.5 + x = -13.425721582 Solving 12.5 + x = -13.425721582 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 = -13.425721582 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.425721582 + -12.5 x = -13.425721582 + -12.5 Combine like terms: -13.425721582 + -12.5 = -25.925721582 x = -25.925721582 Simplifying x = -25.925721582

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.925721582, -25.925721582}

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