2r^2+3r-10=0

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Solution for 2r^2+3r-10=0 equation:


Simplifying
2r2 + 3r + -10 = 0

Reorder the terms:
-10 + 3r + 2r2 = 0

Solving
-10 + 3r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
-5 + 1.5r + r2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 1.5r + 5 + r2 = 0 + 5

Reorder the terms:
-5 + 5 + 1.5r + r2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 1.5r + r2 = 0 + 5
1.5r + r2 = 0 + 5

Combine like terms: 0 + 5 = 5
1.5r + r2 = 5

The r term is 1.5r.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5r + 0.5625 + r2 = 5 + 0.5625

Reorder the terms:
0.5625 + 1.5r + r2 = 5 + 0.5625

Combine like terms: 5 + 0.5625 = 5.5625
0.5625 + 1.5r + r2 = 5.5625

Factor a perfect square on the left side:
(r + 0.75)(r + 0.75) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(r + 0.75) equal to 2.358495283 and -2.358495283.

Subproblem 1

r + 0.75 = 2.358495283 Simplifying r + 0.75 = 2.358495283 Reorder the terms: 0.75 + r = 2.358495283 Solving 0.75 + r = 2.358495283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = 2.358495283 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = 2.358495283 + -0.75 r = 2.358495283 + -0.75 Combine like terms: 2.358495283 + -0.75 = 1.608495283 r = 1.608495283 Simplifying r = 1.608495283

Subproblem 2

r + 0.75 = -2.358495283 Simplifying r + 0.75 = -2.358495283 Reorder the terms: 0.75 + r = -2.358495283 Solving 0.75 + r = -2.358495283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + r = -2.358495283 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + r = -2.358495283 + -0.75 r = -2.358495283 + -0.75 Combine like terms: -2.358495283 + -0.75 = -3.108495283 r = -3.108495283 Simplifying r = -3.108495283

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.608495283, -3.108495283}

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