7r^2+14r-26=-7

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Solution for 7r^2+14r-26=-7 equation:


Simplifying
7r2 + 14r + -26 = -7

Reorder the terms:
-26 + 14r + 7r2 = -7

Solving
-26 + 14r + 7r2 = -7

Solving for variable 'r'.

Reorder the terms:
-26 + 7 + 14r + 7r2 = -7 + 7

Combine like terms: -26 + 7 = -19
-19 + 14r + 7r2 = -7 + 7

Combine like terms: -7 + 7 = 0
-19 + 14r + 7r2 = 0

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

Divide each side by '7'.
-2.714285714 + 2r + r2 = 0

Move the constant term to the right:

Add '2.714285714' to each side of the equation.
-2.714285714 + 2r + 2.714285714 + r2 = 0 + 2.714285714

Reorder the terms:
-2.714285714 + 2.714285714 + 2r + r2 = 0 + 2.714285714

Combine like terms: -2.714285714 + 2.714285714 = 0.000000000
0.000000000 + 2r + r2 = 0 + 2.714285714
2r + r2 = 0 + 2.714285714

Combine like terms: 0 + 2.714285714 = 2.714285714
2r + r2 = 2.714285714

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 2.714285714 + 1

Reorder the terms:
1 + 2r + r2 = 2.714285714 + 1

Combine like terms: 2.714285714 + 1 = 3.714285714
1 + 2r + r2 = 3.714285714

Factor a perfect square on the left side:
(r + 1)(r + 1) = 3.714285714

Calculate the square root of the right side: 1.927248223

Break this problem into two subproblems by setting 
(r + 1) equal to 1.927248223 and -1.927248223.

Subproblem 1

r + 1 = 1.927248223 Simplifying r + 1 = 1.927248223 Reorder the terms: 1 + r = 1.927248223 Solving 1 + r = 1.927248223 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 1.927248223 + -1 Combine like terms: 1 + -1 = 0 0 + r = 1.927248223 + -1 r = 1.927248223 + -1 Combine like terms: 1.927248223 + -1 = 0.927248223 r = 0.927248223 Simplifying r = 0.927248223

Subproblem 2

r + 1 = -1.927248223 Simplifying r + 1 = -1.927248223 Reorder the terms: 1 + r = -1.927248223 Solving 1 + r = -1.927248223 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -1.927248223 + -1 Combine like terms: 1 + -1 = 0 0 + r = -1.927248223 + -1 r = -1.927248223 + -1 Combine like terms: -1.927248223 + -1 = -2.927248223 r = -2.927248223 Simplifying r = -2.927248223

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.927248223, -2.927248223}

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