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Simplifying 9r2 + 12r + 13 = 0 Reorder the terms: 13 + 12r + 9r2 = 0 Solving 13 + 12r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 1.333333333r + r2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 1.333333333r + -1.444444444 + r2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 1.333333333r + r2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 1.333333333r + r2 = 0 + -1.444444444 1.333333333r + r2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 1.333333333r + r2 = -1.444444444 The r term is 1.333333333r. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333r + 0.4444444442 + r2 = -1.444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333r + r2 = -1.444444444 + 0.4444444442 Combine like terms: -1.444444444 + 0.4444444442 = -0.9999999998 0.4444444442 + 1.333333333r + r2 = -0.9999999998 Factor a perfect square on the left side: (r + 0.6666666665)(r + 0.6666666665) = -0.9999999998 Can't calculate square root of the right side. The solution to this equation could not be determined.
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