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Simplifying -10r2 + -3r + 12 = 0 Reorder the terms: 12 + -3r + -10r2 = 0 Solving 12 + -3r + -10r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.2 + 0.3r + r2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.3r + 1.2 + r2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.3r + r2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.3r + r2 = 0 + 1.2 0.3r + r2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.3r + r2 = 1.2 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 = 1.2 + 0.0225 Reorder the terms: 0.0225 + 0.3r + r2 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + 0.3r + r2 = 1.2225 Factor a perfect square on the left side: (r + 0.15)(r + 0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (r + 0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
r + 0.15 = 1.105667219 Simplifying r + 0.15 = 1.105667219 Reorder the terms: 0.15 + r = 1.105667219 Solving 0.15 + r = 1.105667219 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 = 1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + r = 1.105667219 + -0.15 r = 1.105667219 + -0.15 Combine like terms: 1.105667219 + -0.15 = 0.955667219 r = 0.955667219 Simplifying r = 0.955667219Subproblem 2
r + 0.15 = -1.105667219 Simplifying r + 0.15 = -1.105667219 Reorder the terms: 0.15 + r = -1.105667219 Solving 0.15 + r = -1.105667219 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 = -1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + r = -1.105667219 + -0.15 r = -1.105667219 + -0.15 Combine like terms: -1.105667219 + -0.15 = -1.255667219 r = -1.255667219 Simplifying r = -1.255667219Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.955667219, -1.255667219}
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