4r^2-7r-10=0

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Solution for 4r^2-7r-10=0 equation:


Simplifying
4r2 + -7r + -10 = 0

Reorder the terms:
-10 + -7r + 4r2 = 0

Solving
-10 + -7r + 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'.
-2.5 + -1.75r + r2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1.75r + 2.5 + r2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1.75r + r2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1.75r + r2 = 0 + 2.5
-1.75r + r2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1.75r + r2 = 2.5

The r term is -1.75r.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75r + 0.765625 + r2 = 2.5 + 0.765625

Reorder the terms:
0.765625 + -1.75r + r2 = 2.5 + 0.765625

Combine like terms: 2.5 + 0.765625 = 3.265625
0.765625 + -1.75r + r2 = 3.265625

Factor a perfect square on the left side:
(r + -0.875)(r + -0.875) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(r + -0.875) equal to 1.807104037 and -1.807104037.

Subproblem 1

r + -0.875 = 1.807104037 Simplifying r + -0.875 = 1.807104037 Reorder the terms: -0.875 + r = 1.807104037 Solving -0.875 + r = 1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = 1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = 1.807104037 + 0.875 r = 1.807104037 + 0.875 Combine like terms: 1.807104037 + 0.875 = 2.682104037 r = 2.682104037 Simplifying r = 2.682104037

Subproblem 2

r + -0.875 = -1.807104037 Simplifying r + -0.875 = -1.807104037 Reorder the terms: -0.875 + r = -1.807104037 Solving -0.875 + r = -1.807104037 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + r = -1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + r = -1.807104037 + 0.875 r = -1.807104037 + 0.875 Combine like terms: -1.807104037 + 0.875 = -0.932104037 r = -0.932104037 Simplifying r = -0.932104037

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.682104037, -0.932104037}

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