5r^2+7r-62=-4

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Solution for 5r^2+7r-62=-4 equation:


Simplifying
5r2 + 7r + -62 = -4

Reorder the terms:
-62 + 7r + 5r2 = -4

Solving
-62 + 7r + 5r2 = -4

Solving for variable 'r'.

Reorder the terms:
-62 + 4 + 7r + 5r2 = -4 + 4

Combine like terms: -62 + 4 = -58
-58 + 7r + 5r2 = -4 + 4

Combine like terms: -4 + 4 = 0
-58 + 7r + 5r2 = 0

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

Divide each side by '5'.
-11.6 + 1.4r + r2 = 0

Move the constant term to the right:

Add '11.6' to each side of the equation.
-11.6 + 1.4r + 11.6 + r2 = 0 + 11.6

Reorder the terms:
-11.6 + 11.6 + 1.4r + r2 = 0 + 11.6

Combine like terms: -11.6 + 11.6 = 0.0
0.0 + 1.4r + r2 = 0 + 11.6
1.4r + r2 = 0 + 11.6

Combine like terms: 0 + 11.6 = 11.6
1.4r + r2 = 11.6

The r term is 1.4r.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4r + 0.49 + r2 = 11.6 + 0.49

Reorder the terms:
0.49 + 1.4r + r2 = 11.6 + 0.49

Combine like terms: 11.6 + 0.49 = 12.09
0.49 + 1.4r + r2 = 12.09

Factor a perfect square on the left side:
(r + 0.7)(r + 0.7) = 12.09

Calculate the square root of the right side: 3.47706773

Break this problem into two subproblems by setting 
(r + 0.7) equal to 3.47706773 and -3.47706773.

Subproblem 1

r + 0.7 = 3.47706773 Simplifying r + 0.7 = 3.47706773 Reorder the terms: 0.7 + r = 3.47706773 Solving 0.7 + r = 3.47706773 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = 3.47706773 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = 3.47706773 + -0.7 r = 3.47706773 + -0.7 Combine like terms: 3.47706773 + -0.7 = 2.77706773 r = 2.77706773 Simplifying r = 2.77706773

Subproblem 2

r + 0.7 = -3.47706773 Simplifying r + 0.7 = -3.47706773 Reorder the terms: 0.7 + r = -3.47706773 Solving 0.7 + r = -3.47706773 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = -3.47706773 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = -3.47706773 + -0.7 r = -3.47706773 + -0.7 Combine like terms: -3.47706773 + -0.7 = -4.17706773 r = -4.17706773 Simplifying r = -4.17706773

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.77706773, -4.17706773}

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