7r^2-14=10r

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Solution for 7r^2-14=10r equation:


Simplifying
7r2 + -14 = 10r

Reorder the terms:
-14 + 7r2 = 10r

Solving
-14 + 7r2 = 10r

Solving for variable 'r'.

Reorder the terms:
-14 + -10r + 7r2 = 10r + -10r

Combine like terms: 10r + -10r = 0
-14 + -10r + 7r2 = 0

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

Divide each side by '7'.
-2 + -1.428571429r + r2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.428571429r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.428571429r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.428571429r + r2 = 0 + 2
-1.428571429r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.428571429r + r2 = 2

The r term is -1.428571429r.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429r + 0.5102040819 + r2 = 2 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429r + r2 = 2 + 0.5102040819

Combine like terms: 2 + 0.5102040819 = 2.5102040819
0.5102040819 + -1.428571429r + r2 = 2.5102040819

Factor a perfect square on the left side:
(r + -0.7142857145)(r + -0.7142857145) = 2.5102040819

Calculate the square root of the right side: 1.584362358

Break this problem into two subproblems by setting 
(r + -0.7142857145) equal to 1.584362358 and -1.584362358.

Subproblem 1

r + -0.7142857145 = 1.584362358 Simplifying r + -0.7142857145 = 1.584362358 Reorder the terms: -0.7142857145 + r = 1.584362358 Solving -0.7142857145 + r = 1.584362358 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + r = 1.584362358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + r = 1.584362358 + 0.7142857145 r = 1.584362358 + 0.7142857145 Combine like terms: 1.584362358 + 0.7142857145 = 2.2986480725 r = 2.2986480725 Simplifying r = 2.2986480725

Subproblem 2

r + -0.7142857145 = -1.584362358 Simplifying r + -0.7142857145 = -1.584362358 Reorder the terms: -0.7142857145 + r = -1.584362358 Solving -0.7142857145 + r = -1.584362358 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + r = -1.584362358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + r = -1.584362358 + 0.7142857145 r = -1.584362358 + 0.7142857145 Combine like terms: -1.584362358 + 0.7142857145 = -0.8700766435 r = -0.8700766435 Simplifying r = -0.8700766435

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.2986480725, -0.8700766435}

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