r^2-20r-67=7

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Solution for r^2-20r-67=7 equation:


Simplifying
r2 + -20r + -67 = 7

Reorder the terms:
-67 + -20r + r2 = 7

Solving
-67 + -20r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
-67 + -7 + -20r + r2 = 7 + -7

Combine like terms: -67 + -7 = -74
-74 + -20r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-74 + -20r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + -20r + 74 + r2 = 0 + 74

Reorder the terms:
-74 + 74 + -20r + r2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + -20r + r2 = 0 + 74
-20r + r2 = 0 + 74

Combine like terms: 0 + 74 = 74
-20r + r2 = 74

The r term is -20r.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20r + 100 + r2 = 74 + 100

Reorder the terms:
100 + -20r + r2 = 74 + 100

Combine like terms: 74 + 100 = 174
100 + -20r + r2 = 174

Factor a perfect square on the left side:
(r + -10)(r + -10) = 174

Calculate the square root of the right side: 13.190905958

Break this problem into two subproblems by setting 
(r + -10) equal to 13.190905958 and -13.190905958.

Subproblem 1

r + -10 = 13.190905958 Simplifying r + -10 = 13.190905958 Reorder the terms: -10 + r = 13.190905958 Solving -10 + r = 13.190905958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 13.190905958 + 10 Combine like terms: -10 + 10 = 0 0 + r = 13.190905958 + 10 r = 13.190905958 + 10 Combine like terms: 13.190905958 + 10 = 23.190905958 r = 23.190905958 Simplifying r = 23.190905958

Subproblem 2

r + -10 = -13.190905958 Simplifying r + -10 = -13.190905958 Reorder the terms: -10 + r = -13.190905958 Solving -10 + r = -13.190905958 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -13.190905958 + 10 Combine like terms: -10 + 10 = 0 0 + r = -13.190905958 + 10 r = -13.190905958 + 10 Combine like terms: -13.190905958 + 10 = -3.190905958 r = -3.190905958 Simplifying r = -3.190905958

Solution

The solution to the problem is based on the solutions from the subproblems. r = {23.190905958, -3.190905958}

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