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Simplifying 8x2 + 18x + -41 = -10 Reorder the terms: -41 + 18x + 8x2 = -10 Solving -41 + 18x + 8x2 = -10 Solving for variable 'x'. Reorder the terms: -41 + 10 + 18x + 8x2 = -10 + 10 Combine like terms: -41 + 10 = -31 -31 + 18x + 8x2 = -10 + 10 Combine like terms: -10 + 10 = 0 -31 + 18x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.875 + 2.25x + x2 = 0 Move the constant term to the right: Add '3.875' to each side of the equation. -3.875 + 2.25x + 3.875 + x2 = 0 + 3.875 Reorder the terms: -3.875 + 3.875 + 2.25x + x2 = 0 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + 2.25x + x2 = 0 + 3.875 2.25x + x2 = 0 + 3.875 Combine like terms: 0 + 3.875 = 3.875 2.25x + x2 = 3.875 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 = 3.875 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 3.875 + 1.265625 Combine like terms: 3.875 + 1.265625 = 5.140625 1.265625 + 2.25x + x2 = 5.140625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + 1.125) equal to 2.267294643 and -2.267294643.Subproblem 1
x + 1.125 = 2.267294643 Simplifying x + 1.125 = 2.267294643 Reorder the terms: 1.125 + x = 2.267294643 Solving 1.125 + x = 2.267294643 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 = 2.267294643 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.267294643 + -1.125 x = 2.267294643 + -1.125 Combine like terms: 2.267294643 + -1.125 = 1.142294643 x = 1.142294643 Simplifying x = 1.142294643Subproblem 2
x + 1.125 = -2.267294643 Simplifying x + 1.125 = -2.267294643 Reorder the terms: 1.125 + x = -2.267294643 Solving 1.125 + x = -2.267294643 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 = -2.267294643 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.267294643 + -1.125 x = -2.267294643 + -1.125 Combine like terms: -2.267294643 + -1.125 = -3.392294643 x = -3.392294643 Simplifying x = -3.392294643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.142294643, -3.392294643}
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