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Simplifying 4r2 + -8r = 3 Reorder the terms: -8r + 4r2 = 3 Solving -8r + 4r2 = 3 Solving for variable 'r'. Reorder the terms: -3 + -8r + 4r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8r + 4r2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -2r + r2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2r + 0.75 + r2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2r + r2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2r + r2 = 0 + 0.75 -2r + r2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2r + r2 = 0.75 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 = 0.75 + 1 Reorder the terms: 1 + -2r + r2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + -2r + r2 = 1.75 Factor a perfect square on the left side: (r + -1)(r + -1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (r + -1) equal to 1.322875656 and -1.322875656.Subproblem 1
r + -1 = 1.322875656 Simplifying r + -1 = 1.322875656 Reorder the terms: -1 + r = 1.322875656 Solving -1 + r = 1.322875656 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 = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + r = 1.322875656 + 1 r = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 r = 2.322875656 Simplifying r = 2.322875656Subproblem 2
r + -1 = -1.322875656 Simplifying r + -1 = -1.322875656 Reorder the terms: -1 + r = -1.322875656 Solving -1 + r = -1.322875656 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 = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + r = -1.322875656 + 1 r = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 r = -0.322875656 Simplifying r = -0.322875656Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.322875656, -0.322875656}
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