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Simplifying 8x2 + -18x + 1 = 0 Reorder the terms: 1 + -18x + 8x2 = 0 Solving 1 + -18x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -2.25x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -2.25x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -2.25x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -2.25x + x2 = 0 + -0.125 -2.25x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -2.25x + x2 = -0.125 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -0.125 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -0.125 + 1.265625 Combine like terms: -0.125 + 1.265625 = 1.140625 1.265625 + -2.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -1.125) equal to 1.068000468 and -1.068000468.Subproblem 1
x + -1.125 = 1.068000468 Simplifying x + -1.125 = 1.068000468 Reorder the terms: -1.125 + x = 1.068000468 Solving -1.125 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.068000468 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.068000468 + 1.125 x = 1.068000468 + 1.125 Combine like terms: 1.068000468 + 1.125 = 2.193000468 x = 2.193000468 Simplifying x = 2.193000468Subproblem 2
x + -1.125 = -1.068000468 Simplifying x + -1.125 = -1.068000468 Reorder the terms: -1.125 + x = -1.068000468 Solving -1.125 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.068000468 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.068000468 + 1.125 x = -1.068000468 + 1.125 Combine like terms: -1.068000468 + 1.125 = 0.056999532 x = 0.056999532 Simplifying x = 0.056999532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.193000468, 0.056999532}
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