4r^2-15r+7=0

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Solution for 4r^2-15r+7=0 equation:


Simplifying
4r2 + -15r + 7 = 0

Reorder the terms:
7 + -15r + 4r2 = 0

Solving
7 + -15r + 4r2 = 0

Solving for variable 'r'.

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

Divide each side by '4'.
1.75 + -3.75r + r2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -3.75r + -1.75 + r2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -3.75r + r2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -3.75r + r2 = 0 + -1.75
-3.75r + r2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-3.75r + r2 = -1.75

The r term is -3.75r.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75r + 3.515625 + r2 = -1.75 + 3.515625

Reorder the terms:
3.515625 + -3.75r + r2 = -1.75 + 3.515625

Combine like terms: -1.75 + 3.515625 = 1.765625
3.515625 + -3.75r + r2 = 1.765625

Factor a perfect square on the left side:
(r + -1.875)(r + -1.875) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(r + -1.875) equal to 1.328768227 and -1.328768227.

Subproblem 1

r + -1.875 = 1.328768227 Simplifying r + -1.875 = 1.328768227 Reorder the terms: -1.875 + r = 1.328768227 Solving -1.875 + r = 1.328768227 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + r = 1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + r = 1.328768227 + 1.875 r = 1.328768227 + 1.875 Combine like terms: 1.328768227 + 1.875 = 3.203768227 r = 3.203768227 Simplifying r = 3.203768227

Subproblem 2

r + -1.875 = -1.328768227 Simplifying r + -1.875 = -1.328768227 Reorder the terms: -1.875 + r = -1.328768227 Solving -1.875 + r = -1.328768227 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + r = -1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + r = -1.328768227 + 1.875 r = -1.328768227 + 1.875 Combine like terms: -1.328768227 + 1.875 = 0.546231773 r = 0.546231773 Simplifying r = 0.546231773

Solution

The solution to the problem is based on the solutions from the subproblems. r = {3.203768227, 0.546231773}

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