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Simplifying 13r + -28 = 4r2 + -12 Reorder the terms: -28 + 13r = 4r2 + -12 Reorder the terms: -28 + 13r = -12 + 4r2 Solving -28 + 13r = -12 + 4r2 Solving for variable 'r'. Reorder the terms: -28 + 12 + 13r + -4r2 = -12 + 4r2 + 12 + -4r2 Combine like terms: -28 + 12 = -16 -16 + 13r + -4r2 = -12 + 4r2 + 12 + -4r2 Reorder the terms: -16 + 13r + -4r2 = -12 + 12 + 4r2 + -4r2 Combine like terms: -12 + 12 = 0 -16 + 13r + -4r2 = 0 + 4r2 + -4r2 -16 + 13r + -4r2 = 4r2 + -4r2 Combine like terms: 4r2 + -4r2 = 0 -16 + 13r + -4r2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 4 + -3.25r + r2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3.25r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + -3.25r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3.25r + r2 = 0 + -4 -3.25r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3.25r + r2 = -4 The r term is -3.25r. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25r + 2.640625 + r2 = -4 + 2.640625 Reorder the terms: 2.640625 + -3.25r + r2 = -4 + 2.640625 Combine like terms: -4 + 2.640625 = -1.359375 2.640625 + -3.25r + r2 = -1.359375 Factor a perfect square on the left side: (r + -1.625)(r + -1.625) = -1.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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