9r^2-14=-10r

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Solution for 9r^2-14=-10r equation:


Simplifying
9r2 + -14 = -10r

Reorder the terms:
-14 + 9r2 = -10r

Solving
-14 + 9r2 = -10r

Solving for variable 'r'.

Reorder the terms:
-14 + 10r + 9r2 = -10r + 10r

Combine like terms: -10r + 10r = 0
-14 + 10r + 9r2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.555555556 + 1.111111111r + r2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + 1.111111111r + 1.555555556 + r2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + 1.111111111r + r2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + 1.111111111r + r2 = 0 + 1.555555556
1.111111111r + r2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
1.111111111r + r2 = 1.555555556

The r term is 1.111111111r.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111r + 0.3086419752 + r2 = 1.555555556 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111r + r2 = 1.555555556 + 0.3086419752

Combine like terms: 1.555555556 + 0.3086419752 = 1.8641975312
0.3086419752 + 1.111111111r + r2 = 1.8641975312

Factor a perfect square on the left side:
(r + 0.5555555555)(r + 0.5555555555) = 1.8641975312

Calculate the square root of the right side: 1.365356192

Break this problem into two subproblems by setting 
(r + 0.5555555555) equal to 1.365356192 and -1.365356192.

Subproblem 1

r + 0.5555555555 = 1.365356192 Simplifying r + 0.5555555555 = 1.365356192 Reorder the terms: 0.5555555555 + r = 1.365356192 Solving 0.5555555555 + r = 1.365356192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + r = 1.365356192 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + r = 1.365356192 + -0.5555555555 r = 1.365356192 + -0.5555555555 Combine like terms: 1.365356192 + -0.5555555555 = 0.8098006365 r = 0.8098006365 Simplifying r = 0.8098006365

Subproblem 2

r + 0.5555555555 = -1.365356192 Simplifying r + 0.5555555555 = -1.365356192 Reorder the terms: 0.5555555555 + r = -1.365356192 Solving 0.5555555555 + r = -1.365356192 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + r = -1.365356192 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + r = -1.365356192 + -0.5555555555 r = -1.365356192 + -0.5555555555 Combine like terms: -1.365356192 + -0.5555555555 = -1.9209117475 r = -1.9209117475 Simplifying r = -1.9209117475

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.8098006365, -1.9209117475}

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