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Simplifying 0 = r2 + -4r + 45 Reorder the terms: 0 = 45 + -4r + r2 Solving 0 = 45 + -4r + r2 Solving for variable 'r'. Combine like terms: 0 + -45 = -45 -45 + 4r + -1r2 = 45 + -4r + r2 + -45 + 4r + -1r2 Reorder the terms: -45 + 4r + -1r2 = 45 + -45 + -4r + 4r + r2 + -1r2 Combine like terms: 45 + -45 = 0 -45 + 4r + -1r2 = 0 + -4r + 4r + r2 + -1r2 -45 + 4r + -1r2 = -4r + 4r + r2 + -1r2 Combine like terms: -4r + 4r = 0 -45 + 4r + -1r2 = 0 + r2 + -1r2 -45 + 4r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -45 + 4r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 45 + -4r + r2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -4r + -45 + r2 = 0 + -45 Reorder the terms: 45 + -45 + -4r + r2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -4r + r2 = 0 + -45 -4r + r2 = 0 + -45 Combine like terms: 0 + -45 = -45 -4r + r2 = -45 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = -45 + 4 Reorder the terms: 4 + -4r + r2 = -45 + 4 Combine like terms: -45 + 4 = -41 4 + -4r + r2 = -41 Factor a perfect square on the left side: (r + -2)(r + -2) = -41 Can't calculate square root of the right side. The solution to this equation could not be determined.
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