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Simplifying 2r2 + -28r + 38 = 0 Reorder the terms: 38 + -28r + 2r2 = 0 Solving 38 + -28r + 2r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -14r + r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -14r + r2)' equal to zero and attempt to solve: Simplifying 19 + -14r + r2 = 0 Solving 19 + -14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14r + -19 + r2 = 0 + -19 Reorder the terms: 19 + -19 + -14r + r2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14r + r2 = 0 + -19 -14r + r2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14r + r2 = -19 The r term is -14r. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14r + 49 + r2 = -19 + 49 Reorder the terms: 49 + -14r + r2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + -14r + r2 = 30 Factor a perfect square on the left side: (r + -7)(r + -7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (r + -7) equal to 5.477225575 and -5.477225575.Subproblem 1
r + -7 = 5.477225575 Simplifying r + -7 = 5.477225575 Reorder the terms: -7 + r = 5.477225575 Solving -7 + r = 5.477225575 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + r = 5.477225575 + 7 r = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 r = 12.477225575 Simplifying r = 12.477225575Subproblem 2
r + -7 = -5.477225575 Simplifying r + -7 = -5.477225575 Reorder the terms: -7 + r = -5.477225575 Solving -7 + r = -5.477225575 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + r = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + r = -5.477225575 + 7 r = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 r = 1.522774425 Simplifying r = 1.522774425Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.477225575, 1.522774425}Solution
r = {12.477225575, 1.522774425}
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