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Simplifying 3r2 + -42r + 110 = 0 Reorder the terms: 110 + -42r + 3r2 = 0 Solving 110 + -42r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 36.66666667 + -14r + r2 = 0 Move the constant term to the right: Add '-36.66666667' to each side of the equation. 36.66666667 + -14r + -36.66666667 + r2 = 0 + -36.66666667 Reorder the terms: 36.66666667 + -36.66666667 + -14r + r2 = 0 + -36.66666667 Combine like terms: 36.66666667 + -36.66666667 = 0.00000000 0.00000000 + -14r + r2 = 0 + -36.66666667 -14r + r2 = 0 + -36.66666667 Combine like terms: 0 + -36.66666667 = -36.66666667 -14r + r2 = -36.66666667 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 = -36.66666667 + 49 Reorder the terms: 49 + -14r + r2 = -36.66666667 + 49 Combine like terms: -36.66666667 + 49 = 12.33333333 49 + -14r + r2 = 12.33333333 Factor a perfect square on the left side: (r + -7)(r + -7) = 12.33333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (r + -7) equal to 3.511884584 and -3.511884584.Subproblem 1
r + -7 = 3.511884584 Simplifying r + -7 = 3.511884584 Reorder the terms: -7 + r = 3.511884584 Solving -7 + r = 3.511884584 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 = 3.511884584 + 7 Combine like terms: -7 + 7 = 0 0 + r = 3.511884584 + 7 r = 3.511884584 + 7 Combine like terms: 3.511884584 + 7 = 10.511884584 r = 10.511884584 Simplifying r = 10.511884584Subproblem 2
r + -7 = -3.511884584 Simplifying r + -7 = -3.511884584 Reorder the terms: -7 + r = -3.511884584 Solving -7 + r = -3.511884584 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 = -3.511884584 + 7 Combine like terms: -7 + 7 = 0 0 + r = -3.511884584 + 7 r = -3.511884584 + 7 Combine like terms: -3.511884584 + 7 = 3.488115416 r = 3.488115416 Simplifying r = 3.488115416Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.511884584, 3.488115416}
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