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Simplifying r2 + -81 = (r + -9)(r + -9) Reorder the terms: -81 + r2 = (r + -9)(r + -9) Reorder the terms: -81 + r2 = (-9 + r)(r + -9) Reorder the terms: -81 + r2 = (-9 + r)(-9 + r) Multiply (-9 + r) * (-9 + r) -81 + r2 = (-9(-9 + r) + r(-9 + r)) -81 + r2 = ((-9 * -9 + r * -9) + r(-9 + r)) -81 + r2 = ((81 + -9r) + r(-9 + r)) -81 + r2 = (81 + -9r + (-9 * r + r * r)) -81 + r2 = (81 + -9r + (-9r + r2)) Combine like terms: -9r + -9r = -18r -81 + r2 = (81 + -18r + r2) Add '-1r2' to each side of the equation. -81 + r2 + -1r2 = 81 + -18r + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -81 + 0 = 81 + -18r + r2 + -1r2 -81 = 81 + -18r + r2 + -1r2 Combine like terms: r2 + -1r2 = 0 -81 = 81 + -18r + 0 -81 = 81 + -18r Solving -81 = 81 + -18r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '18r' to each side of the equation. -81 + 18r = 81 + -18r + 18r Combine like terms: -18r + 18r = 0 -81 + 18r = 81 + 0 -81 + 18r = 81 Add '81' to each side of the equation. -81 + 81 + 18r = 81 + 81 Combine like terms: -81 + 81 = 0 0 + 18r = 81 + 81 18r = 81 + 81 Combine like terms: 81 + 81 = 162 18r = 162 Divide each side by '18'. r = 9 Simplifying r = 9
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