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Simplifying 3r2 + -13r + -7 = 5 Reorder the terms: -7 + -13r + 3r2 = 5 Solving -7 + -13r + 3r2 = 5 Solving for variable 'r'. Reorder the terms: -7 + -5 + -13r + 3r2 = 5 + -5 Combine like terms: -7 + -5 = -12 -12 + -13r + 3r2 = 5 + -5 Combine like terms: 5 + -5 = 0 -12 + -13r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -4.333333333r + r2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.333333333r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + -4.333333333r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.333333333r + r2 = 0 + 4 -4.333333333r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.333333333r + r2 = 4 The r term is -4.333333333r. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333r + 4.694444446 + r2 = 4 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333r + r2 = 4 + 4.694444446 Combine like terms: 4 + 4.694444446 = 8.694444446 4.694444446 + -4.333333333r + r2 = 8.694444446 Factor a perfect square on the left side: (r + -2.166666667)(r + -2.166666667) = 8.694444446 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (r + -2.166666667) equal to 2.948634336 and -2.948634336.Subproblem 1
r + -2.166666667 = 2.948634336 Simplifying r + -2.166666667 = 2.948634336 Reorder the terms: -2.166666667 + r = 2.948634336 Solving -2.166666667 + r = 2.948634336 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + r = 2.948634336 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + r = 2.948634336 + 2.166666667 r = 2.948634336 + 2.166666667 Combine like terms: 2.948634336 + 2.166666667 = 5.115301003 r = 5.115301003 Simplifying r = 5.115301003Subproblem 2
r + -2.166666667 = -2.948634336 Simplifying r + -2.166666667 = -2.948634336 Reorder the terms: -2.166666667 + r = -2.948634336 Solving -2.166666667 + r = -2.948634336 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + r = -2.948634336 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + r = -2.948634336 + 2.166666667 r = -2.948634336 + 2.166666667 Combine like terms: -2.948634336 + 2.166666667 = -0.781967669 r = -0.781967669 Simplifying r = -0.781967669Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.115301003, -0.781967669}
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