r^2=-14-19r

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Solution for r^2=-14-19r equation:


Simplifying
r2 = -14 + -19r

Solving
r2 = -14 + -19r

Solving for variable 'r'.

Reorder the terms:
14 + 19r + r2 = -14 + -19r + 14 + 19r

Reorder the terms:
14 + 19r + r2 = -14 + 14 + -19r + 19r

Combine like terms: -14 + 14 = 0
14 + 19r + r2 = 0 + -19r + 19r
14 + 19r + r2 = -19r + 19r

Combine like terms: -19r + 19r = 0
14 + 19r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 19r + -14 + r2 = 0 + -14

Reorder the terms:
14 + -14 + 19r + r2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 19r + r2 = 0 + -14
19r + r2 = 0 + -14

Combine like terms: 0 + -14 = -14
19r + r2 = -14

The r term is 19r.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19r + 90.25 + r2 = -14 + 90.25

Reorder the terms:
90.25 + 19r + r2 = -14 + 90.25

Combine like terms: -14 + 90.25 = 76.25
90.25 + 19r + r2 = 76.25

Factor a perfect square on the left side:
(r + 9.5)(r + 9.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(r + 9.5) equal to 8.732124598 and -8.732124598.

Subproblem 1

r + 9.5 = 8.732124598 Simplifying r + 9.5 = 8.732124598 Reorder the terms: 9.5 + r = 8.732124598 Solving 9.5 + r = 8.732124598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + r = 8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + r = 8.732124598 + -9.5 r = 8.732124598 + -9.5 Combine like terms: 8.732124598 + -9.5 = -0.767875402 r = -0.767875402 Simplifying r = -0.767875402

Subproblem 2

r + 9.5 = -8.732124598 Simplifying r + 9.5 = -8.732124598 Reorder the terms: 9.5 + r = -8.732124598 Solving 9.5 + r = -8.732124598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + r = -8.732124598 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + r = -8.732124598 + -9.5 r = -8.732124598 + -9.5 Combine like terms: -8.732124598 + -9.5 = -18.232124598 r = -18.232124598 Simplifying r = -18.232124598

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.767875402, -18.232124598}

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