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Simplifying 30 = r * r + 2r Multiply r * r 30 = r2 + 2r Reorder the terms: 30 = 2r + r2 Solving 30 = 2r + r2 Solving for variable 'r'. Reorder the terms: 30 + -2r + -1r2 = 2r + -2r + r2 + -1r2 Combine like terms: 2r + -2r = 0 30 + -2r + -1r2 = 0 + r2 + -1r2 30 + -2r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 30 + -2r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 2r + r2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 2r + 30 + r2 = 0 + 30 Reorder the terms: -30 + 30 + 2r + r2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2r + r2 = 0 + 30 2r + r2 = 0 + 30 Combine like terms: 0 + 30 = 30 2r + r2 = 30 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 30 + 1 Reorder the terms: 1 + 2r + r2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2r + r2 = 31 Factor a perfect square on the left side: (r + 1)(r + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (r + 1) equal to 5.567764363 and -5.567764363.Subproblem 1
r + 1 = 5.567764363 Simplifying r + 1 = 5.567764363 Reorder the terms: 1 + r = 5.567764363 Solving 1 + r = 5.567764363 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + r = 5.567764363 + -1 r = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 r = 4.567764363 Simplifying r = 4.567764363Subproblem 2
r + 1 = -5.567764363 Simplifying r + 1 = -5.567764363 Reorder the terms: 1 + r = -5.567764363 Solving 1 + r = -5.567764363 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + r = -5.567764363 + -1 r = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 r = -6.567764363 Simplifying r = -6.567764363Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.567764363, -6.567764363}
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