r^2-25r-10=0

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Solution for r^2-25r-10=0 equation:


Simplifying
r2 + -25r + -10 = 0

Reorder the terms:
-10 + -25r + r2 = 0

Solving
-10 + -25r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -25r + 10 + r2 = 0 + 10

Reorder the terms:
-10 + 10 + -25r + r2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -25r + r2 = 0 + 10
-25r + r2 = 0 + 10

Combine like terms: 0 + 10 = 10
-25r + r2 = 10

The r term is -25r.  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.
-25r + 156.25 + r2 = 10 + 156.25

Reorder the terms:
156.25 + -25r + r2 = 10 + 156.25

Combine like terms: 10 + 156.25 = 166.25
156.25 + -25r + r2 = 166.25

Factor a perfect square on the left side:
(r + -12.5)(r + -12.5) = 166.25

Calculate the square root of the right side: 12.893796958

Break this problem into two subproblems by setting 
(r + -12.5) equal to 12.893796958 and -12.893796958.

Subproblem 1

r + -12.5 = 12.893796958 Simplifying r + -12.5 = 12.893796958 Reorder the terms: -12.5 + r = 12.893796958 Solving -12.5 + r = 12.893796958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = 12.893796958 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = 12.893796958 + 12.5 r = 12.893796958 + 12.5 Combine like terms: 12.893796958 + 12.5 = 25.393796958 r = 25.393796958 Simplifying r = 25.393796958

Subproblem 2

r + -12.5 = -12.893796958 Simplifying r + -12.5 = -12.893796958 Reorder the terms: -12.5 + r = -12.893796958 Solving -12.5 + r = -12.893796958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + r = -12.893796958 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + r = -12.893796958 + 12.5 r = -12.893796958 + 12.5 Combine like terms: -12.893796958 + 12.5 = -0.393796958 r = -0.393796958 Simplifying r = -0.393796958

Solution

The solution to the problem is based on the solutions from the subproblems. r = {25.393796958, -0.393796958}

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