10r^2=8r+20

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Solution for 10r^2=8r+20 equation:


Simplifying
10r2 = 8r + 20

Reorder the terms:
10r2 = 20 + 8r

Solving
10r2 = 20 + 8r

Solving for variable 'r'.

Reorder the terms:
-20 + -8r + 10r2 = 20 + 8r + -20 + -8r

Reorder the terms:
-20 + -8r + 10r2 = 20 + -20 + 8r + -8r

Combine like terms: 20 + -20 = 0
-20 + -8r + 10r2 = 0 + 8r + -8r
-20 + -8r + 10r2 = 8r + -8r

Combine like terms: 8r + -8r = 0
-20 + -8r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -4r + 5r2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-10 + -4r + 5r2)' equal to zero and attempt to solve: Simplifying -10 + -4r + 5r2 = 0 Solving -10 + -4r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -0.8r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.8r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -0.8r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.8r + r2 = 0 + 2 -0.8r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.8r + r2 = 2 The r term is -0.8r. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8r + 0.16 + r2 = 2 + 0.16 Reorder the terms: 0.16 + -0.8r + r2 = 2 + 0.16 Combine like terms: 2 + 0.16 = 2.16 0.16 + -0.8r + r2 = 2.16 Factor a perfect square on the left side: (r + -0.4)(r + -0.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (r + -0.4) equal to 1.469693846 and -1.469693846.

Subproblem 1

r + -0.4 = 1.469693846 Simplifying r + -0.4 = 1.469693846 Reorder the terms: -0.4 + r = 1.469693846 Solving -0.4 + r = 1.469693846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + r = 1.469693846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + r = 1.469693846 + 0.4 r = 1.469693846 + 0.4 Combine like terms: 1.469693846 + 0.4 = 1.869693846 r = 1.869693846 Simplifying r = 1.869693846

Subproblem 2

r + -0.4 = -1.469693846 Simplifying r + -0.4 = -1.469693846 Reorder the terms: -0.4 + r = -1.469693846 Solving -0.4 + r = -1.469693846 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + r = -1.469693846 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + r = -1.469693846 + 0.4 r = -1.469693846 + 0.4 Combine like terms: -1.469693846 + 0.4 = -1.069693846 r = -1.069693846 Simplifying r = -1.069693846

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.869693846, -1.069693846}

Solution

r = {1.869693846, -1.069693846}

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