r^2-7r-10=0

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Solution for r^2-7r-10=0 equation:


Simplifying
r2 + -7r + -10 = 0

Reorder the terms:
-10 + -7r + r2 = 0

Solving
-10 + -7r + 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 + -7r + 10 + r2 = 0 + 10

Reorder the terms:
-10 + 10 + -7r + r2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7r + r2 = 0 + 10
-7r + r2 = 0 + 10

Combine like terms: 0 + 10 = 10
-7r + r2 = 10

The r term is -7r.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7r + 12.25 + r2 = 10 + 12.25

Reorder the terms:
12.25 + -7r + r2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + -7r + r2 = 22.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(r + -3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

r + -3.5 = 4.716990566 Simplifying r + -3.5 = 4.716990566 Reorder the terms: -3.5 + r = 4.716990566 Solving -3.5 + r = 4.716990566 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = 4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 4.716990566 + 3.5 r = 4.716990566 + 3.5 Combine like terms: 4.716990566 + 3.5 = 8.216990566 r = 8.216990566 Simplifying r = 8.216990566

Subproblem 2

r + -3.5 = -4.716990566 Simplifying r + -3.5 = -4.716990566 Reorder the terms: -3.5 + r = -4.716990566 Solving -3.5 + r = -4.716990566 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + r = -4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -4.716990566 + 3.5 r = -4.716990566 + 3.5 Combine like terms: -4.716990566 + 3.5 = -1.216990566 r = -1.216990566 Simplifying r = -1.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.216990566, -1.216990566}

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