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Simplifying 2r2 + -4r = 15 Reorder the terms: -4r + 2r2 = 15 Solving -4r + 2r2 = 15 Solving for variable 'r'. Reorder the terms: -15 + -4r + 2r2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -4r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -2r + r2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -2r + 7.5 + r2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -2r + r2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -2r + r2 = 0 + 7.5 -2r + r2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -2r + r2 = 7.5 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 = 7.5 + 1 Reorder the terms: 1 + -2r + r2 = 7.5 + 1 Combine like terms: 7.5 + 1 = 8.5 1 + -2r + r2 = 8.5 Factor a perfect square on the left side: (r + -1)(r + -1) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (r + -1) equal to 2.915475947 and -2.915475947.Subproblem 1
r + -1 = 2.915475947 Simplifying r + -1 = 2.915475947 Reorder the terms: -1 + r = 2.915475947 Solving -1 + r = 2.915475947 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 = 2.915475947 + 1 Combine like terms: -1 + 1 = 0 0 + r = 2.915475947 + 1 r = 2.915475947 + 1 Combine like terms: 2.915475947 + 1 = 3.915475947 r = 3.915475947 Simplifying r = 3.915475947Subproblem 2
r + -1 = -2.915475947 Simplifying r + -1 = -2.915475947 Reorder the terms: -1 + r = -2.915475947 Solving -1 + r = -2.915475947 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 = -2.915475947 + 1 Combine like terms: -1 + 1 = 0 0 + r = -2.915475947 + 1 r = -2.915475947 + 1 Combine like terms: -2.915475947 + 1 = -1.915475947 r = -1.915475947 Simplifying r = -1.915475947Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.915475947, -1.915475947}
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