4r^2+24r=-17

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Solution for 4r^2+24r=-17 equation:


Simplifying
4r2 + 24r = -17

Reorder the terms:
24r + 4r2 = -17

Solving
24r + 4r2 = -17

Solving for variable 'r'.

Reorder the terms:
17 + 24r + 4r2 = -17 + 17

Combine like terms: -17 + 17 = 0
17 + 24r + 4r2 = 0

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

Divide each side by '4'.
4.25 + 6r + r2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 6r + -4.25 + r2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 6r + r2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 6r + r2 = 0 + -4.25
6r + r2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
6r + r2 = -4.25

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = -4.25 + 9

Reorder the terms:
9 + 6r + r2 = -4.25 + 9

Combine like terms: -4.25 + 9 = 4.75
9 + 6r + r2 = 4.75

Factor a perfect square on the left side:
(r + 3)(r + 3) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(r + 3) equal to 2.179449472 and -2.179449472.

Subproblem 1

r + 3 = 2.179449472 Simplifying r + 3 = 2.179449472 Reorder the terms: 3 + r = 2.179449472 Solving 3 + r = 2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 2.179449472 + -3 Combine like terms: 3 + -3 = 0 0 + r = 2.179449472 + -3 r = 2.179449472 + -3 Combine like terms: 2.179449472 + -3 = -0.820550528 r = -0.820550528 Simplifying r = -0.820550528

Subproblem 2

r + 3 = -2.179449472 Simplifying r + 3 = -2.179449472 Reorder the terms: 3 + r = -2.179449472 Solving 3 + r = -2.179449472 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -2.179449472 + -3 Combine like terms: 3 + -3 = 0 0 + r = -2.179449472 + -3 r = -2.179449472 + -3 Combine like terms: -2.179449472 + -3 = -5.179449472 r = -5.179449472 Simplifying r = -5.179449472

Solution

The solution to the problem is based on the solutions from the subproblems. r = {-0.820550528, -5.179449472}

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