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Simplifying 0 = 5r2 + -8r + 7 Reorder the terms: 0 = 7 + -8r + 5r2 Solving 0 = 7 + -8r + 5r2 Solving for variable 'r'. Combine like terms: 0 + -7 = -7 -7 + 8r + -5r2 = 7 + -8r + 5r2 + -7 + 8r + -5r2 Reorder the terms: -7 + 8r + -5r2 = 7 + -7 + -8r + 8r + 5r2 + -5r2 Combine like terms: 7 + -7 = 0 -7 + 8r + -5r2 = 0 + -8r + 8r + 5r2 + -5r2 -7 + 8r + -5r2 = -8r + 8r + 5r2 + -5r2 Combine like terms: -8r + 8r = 0 -7 + 8r + -5r2 = 0 + 5r2 + -5r2 -7 + 8r + -5r2 = 5r2 + -5r2 Combine like terms: 5r2 + -5r2 = 0 -7 + 8r + -5r2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.4 + -1.6r + r2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -1.6r + -1.4 + r2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -1.6r + r2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -1.6r + r2 = 0 + -1.4 -1.6r + r2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -1.6r + r2 = -1.4 The r term is -1.6r. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6r + 0.64 + r2 = -1.4 + 0.64 Reorder the terms: 0.64 + -1.6r + r2 = -1.4 + 0.64 Combine like terms: -1.4 + 0.64 = -0.76 0.64 + -1.6r + r2 = -0.76 Factor a perfect square on the left side: (r + -0.8)(r + -0.8) = -0.76 Can't calculate square root of the right side. The solution to this equation could not be determined.
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