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Simplifying 10r2 = -12r + 5 Reorder the terms: 10r2 = 5 + -12r Solving 10r2 = 5 + -12r Solving for variable 'r'. Reorder the terms: -5 + 12r + 10r2 = 5 + -12r + -5 + 12r Reorder the terms: -5 + 12r + 10r2 = 5 + -5 + -12r + 12r Combine like terms: 5 + -5 = 0 -5 + 12r + 10r2 = 0 + -12r + 12r -5 + 12r + 10r2 = -12r + 12r Combine like terms: -12r + 12r = 0 -5 + 12r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 1.2r + r2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.2r + 0.5 + r2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.2r + r2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.2r + r2 = 0 + 0.5 1.2r + r2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.2r + r2 = 0.5 The r term is 1.2r. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2r + 0.36 + r2 = 0.5 + 0.36 Reorder the terms: 0.36 + 1.2r + r2 = 0.5 + 0.36 Combine like terms: 0.5 + 0.36 = 0.86 0.36 + 1.2r + r2 = 0.86 Factor a perfect square on the left side: (r + 0.6)(r + 0.6) = 0.86 Calculate the square root of the right side: 0.92736185 Break this problem into two subproblems by setting (r + 0.6) equal to 0.92736185 and -0.92736185.Subproblem 1
r + 0.6 = 0.92736185 Simplifying r + 0.6 = 0.92736185 Reorder the terms: 0.6 + r = 0.92736185 Solving 0.6 + r = 0.92736185 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + r = 0.92736185 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + r = 0.92736185 + -0.6 r = 0.92736185 + -0.6 Combine like terms: 0.92736185 + -0.6 = 0.32736185 r = 0.32736185 Simplifying r = 0.32736185Subproblem 2
r + 0.6 = -0.92736185 Simplifying r + 0.6 = -0.92736185 Reorder the terms: 0.6 + r = -0.92736185 Solving 0.6 + r = -0.92736185 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + r = -0.92736185 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + r = -0.92736185 + -0.6 r = -0.92736185 + -0.6 Combine like terms: -0.92736185 + -0.6 = -1.52736185 r = -1.52736185 Simplifying r = -1.52736185Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.32736185, -1.52736185}
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