-7r^2-20r+100=0

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Solution for -7r^2-20r+100=0 equation:


Simplifying
-7r2 + -20r + 100 = 0

Reorder the terms:
100 + -20r + -7r2 = 0

Solving
100 + -20r + -7r2 = 0

Solving for variable 'r'.

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

Divide each side by '-7'.
-14.28571429 + 2.857142857r + r2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + 2.857142857r + 14.28571429 + r2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + 2.857142857r + r2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + 2.857142857r + r2 = 0 + 14.28571429
2.857142857r + r2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
2.857142857r + r2 = 14.28571429

The r term is 2.857142857r.  Take half its coefficient (1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
2.857142857r + 2.040816328 + r2 = 14.28571429 + 2.040816328

Reorder the terms:
2.040816328 + 2.857142857r + r2 = 14.28571429 + 2.040816328

Combine like terms: 14.28571429 + 2.040816328 = 16.326530618
2.040816328 + 2.857142857r + r2 = 16.326530618

Factor a perfect square on the left side:
(r + 1.428571429)(r + 1.428571429) = 16.326530618

Calculate the square root of the right side: 4.040610179

Break this problem into two subproblems by setting 
(r + 1.428571429) equal to 4.040610179 and -4.040610179.

Subproblem 1

r + 1.428571429 = 4.040610179 Simplifying r + 1.428571429 = 4.040610179 Reorder the terms: 1.428571429 + r = 4.040610179 Solving 1.428571429 + r = 4.040610179 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + r = 4.040610179 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + r = 4.040610179 + -1.428571429 r = 4.040610179 + -1.428571429 Combine like terms: 4.040610179 + -1.428571429 = 2.61203875 r = 2.61203875 Simplifying r = 2.61203875

Subproblem 2

r + 1.428571429 = -4.040610179 Simplifying r + 1.428571429 = -4.040610179 Reorder the terms: 1.428571429 + r = -4.040610179 Solving 1.428571429 + r = -4.040610179 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + r = -4.040610179 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + r = -4.040610179 + -1.428571429 r = -4.040610179 + -1.428571429 Combine like terms: -4.040610179 + -1.428571429 = -5.469181608 r = -5.469181608 Simplifying r = -5.469181608

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.61203875, -5.469181608}

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