3r^2-72r=-123

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Solution for 3r^2-72r=-123 equation:


Simplifying
3r2 + -72r = -123

Reorder the terms:
-72r + 3r2 = -123

Solving
-72r + 3r2 = -123

Solving for variable 'r'.

Reorder the terms:
123 + -72r + 3r2 = -123 + 123

Combine like terms: -123 + 123 = 0
123 + -72r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(41 + -24r + r2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(41 + -24r + r2)' equal to zero and attempt to solve: Simplifying 41 + -24r + r2 = 0 Solving 41 + -24r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -24r + -41 + r2 = 0 + -41 Reorder the terms: 41 + -41 + -24r + r2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -24r + r2 = 0 + -41 -24r + r2 = 0 + -41 Combine like terms: 0 + -41 = -41 -24r + r2 = -41 The r term is -24r. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24r + 144 + r2 = -41 + 144 Reorder the terms: 144 + -24r + r2 = -41 + 144 Combine like terms: -41 + 144 = 103 144 + -24r + r2 = 103 Factor a perfect square on the left side: (r + -12)(r + -12) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (r + -12) equal to 10.148891565 and -10.148891565.

Subproblem 1

r + -12 = 10.148891565 Simplifying r + -12 = 10.148891565 Reorder the terms: -12 + r = 10.148891565 Solving -12 + r = 10.148891565 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = 10.148891565 + 12 Combine like terms: -12 + 12 = 0 0 + r = 10.148891565 + 12 r = 10.148891565 + 12 Combine like terms: 10.148891565 + 12 = 22.148891565 r = 22.148891565 Simplifying r = 22.148891565

Subproblem 2

r + -12 = -10.148891565 Simplifying r + -12 = -10.148891565 Reorder the terms: -12 + r = -10.148891565 Solving -12 + r = -10.148891565 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + r = -10.148891565 + 12 Combine like terms: -12 + 12 = 0 0 + r = -10.148891565 + 12 r = -10.148891565 + 12 Combine like terms: -10.148891565 + 12 = 1.851108435 r = 1.851108435 Simplifying r = 1.851108435

Solution

The solution to the problem is based on the solutions from the subproblems. r = {22.148891565, 1.851108435}

Solution

r = {22.148891565, 1.851108435}

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