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Simplifying 10r2 + -9 = 3r Reorder the terms: -9 + 10r2 = 3r Solving -9 + 10r2 = 3r Solving for variable 'r'. Reorder the terms: -9 + -3r + 10r2 = 3r + -3r Combine like terms: 3r + -3r = 0 -9 + -3r + 10r2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -0.3r + r2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -0.3r + 0.9 + r2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -0.3r + r2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -0.3r + r2 = 0 + 0.9 -0.3r + r2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -0.3r + r2 = 0.9 The r term is -0.3r. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3r + 0.0225 + r2 = 0.9 + 0.0225 Reorder the terms: 0.0225 + -0.3r + r2 = 0.9 + 0.0225 Combine like terms: 0.9 + 0.0225 = 0.9225 0.0225 + -0.3r + r2 = 0.9225 Factor a perfect square on the left side: (r + -0.15)(r + -0.15) = 0.9225 Calculate the square root of the right side: 0.960468636 Break this problem into two subproblems by setting (r + -0.15) equal to 0.960468636 and -0.960468636.Subproblem 1
r + -0.15 = 0.960468636 Simplifying r + -0.15 = 0.960468636 Reorder the terms: -0.15 + r = 0.960468636 Solving -0.15 + r = 0.960468636 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + r = 0.960468636 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + r = 0.960468636 + 0.15 r = 0.960468636 + 0.15 Combine like terms: 0.960468636 + 0.15 = 1.110468636 r = 1.110468636 Simplifying r = 1.110468636Subproblem 2
r + -0.15 = -0.960468636 Simplifying r + -0.15 = -0.960468636 Reorder the terms: -0.15 + r = -0.960468636 Solving -0.15 + r = -0.960468636 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + r = -0.960468636 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + r = -0.960468636 + 0.15 r = -0.960468636 + 0.15 Combine like terms: -0.960468636 + 0.15 = -0.810468636 r = -0.810468636 Simplifying r = -0.810468636Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.110468636, -0.810468636}
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