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Simplifying r2 + -19r + 14 = 0 Reorder the terms: 14 + -19r + r2 = 0 Solving 14 + -19r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -19r + -14 + r2 = 0 + -14 Reorder the terms: 14 + -14 + -19r + r2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -19r + r2 = 0 + -14 -19r + r2 = 0 + -14 Combine like terms: 0 + -14 = -14 -19r + r2 = -14 The r term is -19r. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19r + 90.25 + r2 = -14 + 90.25 Reorder the terms: 90.25 + -19r + r2 = -14 + 90.25 Combine like terms: -14 + 90.25 = 76.25 90.25 + -19r + r2 = 76.25 Factor a perfect square on the left side: (r + -9.5)(r + -9.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (r + -9.5) equal to 8.732124598 and -8.732124598.Subproblem 1
r + -9.5 = 8.732124598 Simplifying r + -9.5 = 8.732124598 Reorder the terms: -9.5 + r = 8.732124598 Solving -9.5 + r = 8.732124598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + r = 8.732124598 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + r = 8.732124598 + 9.5 r = 8.732124598 + 9.5 Combine like terms: 8.732124598 + 9.5 = 18.232124598 r = 18.232124598 Simplifying r = 18.232124598Subproblem 2
r + -9.5 = -8.732124598 Simplifying r + -9.5 = -8.732124598 Reorder the terms: -9.5 + r = -8.732124598 Solving -9.5 + r = -8.732124598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + r = -8.732124598 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + r = -8.732124598 + 9.5 r = -8.732124598 + 9.5 Combine like terms: -8.732124598 + 9.5 = 0.767875402 r = 0.767875402 Simplifying r = 0.767875402Solution
The solution to the problem is based on the solutions from the subproblems. r = {18.232124598, 0.767875402}
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