10r^2+7r-16=0

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Solution for 10r^2+7r-16=0 equation:


Simplifying
10r2 + 7r + -16 = 0

Reorder the terms:
-16 + 7r + 10r2 = 0

Solving
-16 + 7r + 10r2 = 0

Solving for variable 'r'.

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

Divide each side by '10'.
-1.6 + 0.7r + r2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.7r + 1.6 + r2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.7r + r2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.7r + r2 = 0 + 1.6
0.7r + r2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.7r + r2 = 1.6

The r term is 0.7r.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7r + 0.1225 + r2 = 1.6 + 0.1225

Reorder the terms:
0.1225 + 0.7r + r2 = 1.6 + 0.1225

Combine like terms: 1.6 + 0.1225 = 1.7225
0.1225 + 0.7r + r2 = 1.7225

Factor a perfect square on the left side:
(r + 0.35)(r + 0.35) = 1.7225

Calculate the square root of the right side: 1.312440475

Break this problem into two subproblems by setting 
(r + 0.35) equal to 1.312440475 and -1.312440475.

Subproblem 1

r + 0.35 = 1.312440475 Simplifying r + 0.35 = 1.312440475 Reorder the terms: 0.35 + r = 1.312440475 Solving 0.35 + r = 1.312440475 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + r = 1.312440475 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = 1.312440475 + -0.35 r = 1.312440475 + -0.35 Combine like terms: 1.312440475 + -0.35 = 0.962440475 r = 0.962440475 Simplifying r = 0.962440475

Subproblem 2

r + 0.35 = -1.312440475 Simplifying r + 0.35 = -1.312440475 Reorder the terms: 0.35 + r = -1.312440475 Solving 0.35 + r = -1.312440475 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + r = -1.312440475 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + r = -1.312440475 + -0.35 r = -1.312440475 + -0.35 Combine like terms: -1.312440475 + -0.35 = -1.662440475 r = -1.662440475 Simplifying r = -1.662440475

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.962440475, -1.662440475}

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