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Simplifying x2 + -18x + 81 = 2.56 Reorder the terms: 81 + -18x + x2 = 2.56 Solving 81 + -18x + x2 = 2.56 Solving for variable 'x'. Reorder the terms: 81 + -2.56 + -18x + x2 = 2.56 + -2.56 Combine like terms: 81 + -2.56 = 78.44 78.44 + -18x + x2 = 2.56 + -2.56 Combine like terms: 2.56 + -2.56 = 0.00 78.44 + -18x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-78.44' to each side of the equation. 78.44 + -18x + -78.44 + x2 = 0.00 + -78.44 Reorder the terms: 78.44 + -78.44 + -18x + x2 = 0.00 + -78.44 Combine like terms: 78.44 + -78.44 = 0.00 0.00 + -18x + x2 = 0.00 + -78.44 -18x + x2 = 0.00 + -78.44 Combine like terms: 0.00 + -78.44 = -78.44 -18x + x2 = -78.44 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -78.44 + 81 Reorder the terms: 81 + -18x + x2 = -78.44 + 81 Combine like terms: -78.44 + 81 = 2.56 81 + -18x + x2 = 2.56 Factor a perfect square on the left side: (x + -9)(x + -9) = 2.56 Calculate the square root of the right side: 1.6 Break this problem into two subproblems by setting (x + -9) equal to 1.6 and -1.6.Subproblem 1
x + -9 = 1.6 Simplifying x + -9 = 1.6 Reorder the terms: -9 + x = 1.6 Solving -9 + x = 1.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 1.6 + 9 Combine like terms: -9 + 9 = 0 0 + x = 1.6 + 9 x = 1.6 + 9 Combine like terms: 1.6 + 9 = 10.6 x = 10.6 Simplifying x = 10.6Subproblem 2
x + -9 = -1.6 Simplifying x + -9 = -1.6 Reorder the terms: -9 + x = -1.6 Solving -9 + x = -1.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -1.6 + 9 Combine like terms: -9 + 9 = 0 0 + x = -1.6 + 9 x = -1.6 + 9 Combine like terms: -1.6 + 9 = 7.4 x = 7.4 Simplifying x = 7.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.6, 7.4}
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