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Simplifying 81 + (r * r) = (6 + r)(6 + r) Multiply r * r 81 + (r2) = (6 + r)(6 + r) 81 + r2 = (6 + r)(6 + r) Multiply (6 + r) * (6 + r) 81 + r2 = (6(6 + r) + r(6 + r)) 81 + r2 = ((6 * 6 + r * 6) + r(6 + r)) 81 + r2 = ((36 + 6r) + r(6 + r)) 81 + r2 = (36 + 6r + (6 * r + r * r)) 81 + r2 = (36 + 6r + (6r + r2)) Combine like terms: 6r + 6r = 12r 81 + r2 = (36 + 12r + r2) Add '-1r2' to each side of the equation. 81 + r2 + -1r2 = 36 + 12r + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 81 + 0 = 36 + 12r + r2 + -1r2 81 = 36 + 12r + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 81 = 36 + 12r + 0 81 = 36 + 12r Solving 81 = 36 + 12r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-12r' to each side of the equation. 81 + -12r = 36 + 12r + -12r Combine like terms: 12r + -12r = 0 81 + -12r = 36 + 0 81 + -12r = 36 Add '-81' to each side of the equation. 81 + -81 + -12r = 36 + -81 Combine like terms: 81 + -81 = 0 0 + -12r = 36 + -81 -12r = 36 + -81 Combine like terms: 36 + -81 = -45 -12r = -45 Divide each side by '-12'. r = 3.75 Simplifying r = 3.75
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