r^2-9r=14

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Solution for r^2-9r=14 equation:


Simplifying
r2 + -9r = 14

Reorder the terms:
-9r + r2 = 14

Solving
-9r + r2 = 14

Solving for variable 'r'.

Reorder the terms:
-14 + -9r + r2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -9r + 14 + r2 = 0 + 14

Reorder the terms:
-14 + 14 + -9r + r2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -9r + r2 = 0 + 14
-9r + r2 = 0 + 14

Combine like terms: 0 + 14 = 14
-9r + r2 = 14

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = 14 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 14 + 20.25

Combine like terms: 14 + 20.25 = 34.25
20.25 + -9r + r2 = 34.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(r + -4.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

r + -4.5 = 5.852349955 Simplifying r + -4.5 = 5.852349955 Reorder the terms: -4.5 + r = 5.852349955 Solving -4.5 + r = 5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 5.852349955 + 4.5 r = 5.852349955 + 4.5 Combine like terms: 5.852349955 + 4.5 = 10.352349955 r = 10.352349955 Simplifying r = 10.352349955

Subproblem 2

r + -4.5 = -5.852349955 Simplifying r + -4.5 = -5.852349955 Reorder the terms: -4.5 + r = -5.852349955 Solving -4.5 + r = -5.852349955 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -5.852349955 + 4.5 r = -5.852349955 + 4.5 Combine like terms: -5.852349955 + 4.5 = -1.352349955 r = -1.352349955 Simplifying r = -1.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. r = {10.352349955, -1.352349955}

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