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Simplifying -0.6r(r + 0.2) = 18 Reorder the terms: -0.6r(0.2 + r) = 18 (0.2 * -0.6r + r * -0.6r) = 18 (-0.12r + -0.6r2) = 18 Solving -0.12r + -0.6r2 = 18 Solving for variable 'r'. Reorder the terms: -18 + -0.12r + -0.6r2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -0.12r + -0.6r2 = 0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 30 + 0.2r + r2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + 0.2r + -30 + r2 = 0 + -30 Reorder the terms: 30 + -30 + 0.2r + r2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 0.2r + r2 = 0 + -30 0.2r + r2 = 0 + -30 Combine like terms: 0 + -30 = -30 0.2r + r2 = -30 The r term is 0.2r. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2r + 0.01 + r2 = -30 + 0.01 Reorder the terms: 0.01 + 0.2r + r2 = -30 + 0.01 Combine like terms: -30 + 0.01 = -29.99 0.01 + 0.2r + r2 = -29.99 Factor a perfect square on the left side: (r + 0.1)(r + 0.1) = -29.99 Can't calculate square root of the right side. The solution to this equation could not be determined.
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