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Simplifying 5(2 + -3r) * 4r + -123 = 0 Reorder the terms for easier multiplication: 5 * 4r(2 + -3r) + -123 = 0 Multiply 5 * 4 20r(2 + -3r) + -123 = 0 (2 * 20r + -3r * 20r) + -123 = 0 (40r + -60r2) + -123 = 0 Reorder the terms: -123 + 40r + -60r2 = 0 Solving -123 + 40r + -60r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. 2.05 + -0.6666666667r + r2 = 0.0 Move the constant term to the right: Add '-2.05' to each side of the equation. 2.05 + -0.6666666667r + -2.05 + r2 = 0.0 + -2.05 Reorder the terms: 2.05 + -2.05 + -0.6666666667r + r2 = 0.0 + -2.05 Combine like terms: 2.05 + -2.05 = 0.00 0.00 + -0.6666666667r + r2 = 0.0 + -2.05 -0.6666666667r + r2 = 0.0 + -2.05 Combine like terms: 0.0 + -2.05 = -2.05 -0.6666666667r + r2 = -2.05 The r term is -0.6666666667r. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667r + 0.1111111112 + r2 = -2.05 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667r + r2 = -2.05 + 0.1111111112 Combine like terms: -2.05 + 0.1111111112 = -1.9388888888 0.1111111112 + -0.6666666667r + r2 = -1.9388888888 Factor a perfect square on the left side: (r + -0.3333333334)(r + -0.3333333334) = -1.9388888888 Can't calculate square root of the right side. The solution to this equation could not be determined.
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