50r^2+105r-8=0

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Solution for 50r^2+105r-8=0 equation:


Simplifying
50r2 + 105r + -8 = 0

Reorder the terms:
-8 + 105r + 50r2 = 0

Solving
-8 + 105r + 50r2 = 0

Solving for variable 'r'.

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

Divide each side by '50'.
-0.16 + 2.1r + r2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 2.1r + 0.16 + r2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 2.1r + r2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 2.1r + r2 = 0 + 0.16
2.1r + r2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
2.1r + r2 = 0.16

The r term is 2.1r.  Take half its coefficient (1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
2.1r + 1.1025 + r2 = 0.16 + 1.1025

Reorder the terms:
1.1025 + 2.1r + r2 = 0.16 + 1.1025

Combine like terms: 0.16 + 1.1025 = 1.2625
1.1025 + 2.1r + r2 = 1.2625

Factor a perfect square on the left side:
(r + 1.05)(r + 1.05) = 1.2625

Calculate the square root of the right side: 1.123610253

Break this problem into two subproblems by setting 
(r + 1.05) equal to 1.123610253 and -1.123610253.

Subproblem 1

r + 1.05 = 1.123610253 Simplifying r + 1.05 = 1.123610253 Reorder the terms: 1.05 + r = 1.123610253 Solving 1.05 + r = 1.123610253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + r = 1.123610253 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + r = 1.123610253 + -1.05 r = 1.123610253 + -1.05 Combine like terms: 1.123610253 + -1.05 = 0.073610253 r = 0.073610253 Simplifying r = 0.073610253

Subproblem 2

r + 1.05 = -1.123610253 Simplifying r + 1.05 = -1.123610253 Reorder the terms: 1.05 + r = -1.123610253 Solving 1.05 + r = -1.123610253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + r = -1.123610253 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + r = -1.123610253 + -1.05 r = -1.123610253 + -1.05 Combine like terms: -1.123610253 + -1.05 = -2.173610253 r = -2.173610253 Simplifying r = -2.173610253

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.073610253, -2.173610253}

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