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Simplifying (9r2 + 3r + 8) + -1(2r2 + 7) = 0 Reorder the terms: (8 + 3r + 9r2) + -1(2r2 + 7) = 0 Remove parenthesis around (8 + 3r + 9r2) 8 + 3r + 9r2 + -1(2r2 + 7) = 0 Reorder the terms: 8 + 3r + 9r2 + -1(7 + 2r2) = 0 8 + 3r + 9r2 + (7 * -1 + 2r2 * -1) = 0 8 + 3r + 9r2 + (-7 + -2r2) = 0 Reorder the terms: 8 + -7 + 3r + 9r2 + -2r2 = 0 Combine like terms: 8 + -7 = 1 1 + 3r + 9r2 + -2r2 = 0 Combine like terms: 9r2 + -2r2 = 7r2 1 + 3r + 7r2 = 0 Solving 1 + 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'. 0.1428571429 + 0.4285714286r + r2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.4285714286r + -0.1428571429 + r2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.4285714286r + r2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.4285714286r + r2 = 0 + -0.1428571429 0.4285714286r + r2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.4285714286r + r2 = -0.1428571429 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 = -0.1428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286r + r2 = -0.1428571429 + 0.04591836735 Combine like terms: -0.1428571429 + 0.04591836735 = -0.09693877555 0.04591836735 + 0.4285714286r + r2 = -0.09693877555 Factor a perfect square on the left side: (r + 0.2142857143)(r + 0.2142857143) = -0.09693877555 Can't calculate square root of the right side. The solution to this equation could not be determined.
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