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Simplifying 2r2 + 3r + -2 + 5r2 + 8 = 0 Reorder the terms: -2 + 8 + 3r + 2r2 + 5r2 = 0 Combine like terms: -2 + 8 = 6 6 + 3r + 2r2 + 5r2 = 0 Combine like terms: 2r2 + 5r2 = 7r2 6 + 3r + 7r2 = 0 Solving 6 + 3r + 7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 0.4285714286r + r2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 0.4285714286r + -0.8571428571 + r2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 0.4285714286r + r2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 0.4285714286r + r2 = 0 + -0.8571428571 0.4285714286r + r2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 0.4285714286r + r2 = -0.8571428571 The r term is 0.4285714286r. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286r + 0.04591836735 + r2 = -0.8571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286r + r2 = -0.8571428571 + 0.04591836735 Combine like terms: -0.8571428571 + 0.04591836735 = -0.81122448975 0.04591836735 + 0.4285714286r + r2 = -0.81122448975 Factor a perfect square on the left side: (r + 0.2142857143)(r + 0.2142857143) = -0.81122448975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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