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Simplifying 4x2 + -9x + -41 = 0 Reorder the terms: -41 + -9x + 4x2 = 0 Solving -41 + -9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + -2.25x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + -2.25x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + -2.25x + x2 = 0 + 10.25 -2.25x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 -2.25x + x2 = 10.25 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 = 10.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 10.25 + 1.265625 Combine like terms: 10.25 + 1.265625 = 11.515625 1.265625 + -2.25x + x2 = 11.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 11.515625 Calculate the square root of the right side: 3.39346799 Break this problem into two subproblems by setting (x + -1.125) equal to 3.39346799 and -3.39346799.Subproblem 1
x + -1.125 = 3.39346799 Simplifying x + -1.125 = 3.39346799 Reorder the terms: -1.125 + x = 3.39346799 Solving -1.125 + x = 3.39346799 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 = 3.39346799 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 3.39346799 + 1.125 x = 3.39346799 + 1.125 Combine like terms: 3.39346799 + 1.125 = 4.51846799 x = 4.51846799 Simplifying x = 4.51846799Subproblem 2
x + -1.125 = -3.39346799 Simplifying x + -1.125 = -3.39346799 Reorder the terms: -1.125 + x = -3.39346799 Solving -1.125 + x = -3.39346799 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 = -3.39346799 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -3.39346799 + 1.125 x = -3.39346799 + 1.125 Combine like terms: -3.39346799 + 1.125 = -2.26846799 x = -2.26846799 Simplifying x = -2.26846799Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.51846799, -2.26846799}
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