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Simplifying 0 = 4x2 + 9x + -241 Reorder the terms: 0 = -241 + 9x + 4x2 Solving 0 = -241 + 9x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 241 = 241 241 + -9x + -4x2 = -241 + 9x + 4x2 + 241 + -9x + -4x2 Reorder the terms: 241 + -9x + -4x2 = -241 + 241 + 9x + -9x + 4x2 + -4x2 Combine like terms: -241 + 241 = 0 241 + -9x + -4x2 = 0 + 9x + -9x + 4x2 + -4x2 241 + -9x + -4x2 = 9x + -9x + 4x2 + -4x2 Combine like terms: 9x + -9x = 0 241 + -9x + -4x2 = 0 + 4x2 + -4x2 241 + -9x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 241 + -9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -60.25 + 2.25x + x2 = 0 Move the constant term to the right: Add '60.25' to each side of the equation. -60.25 + 2.25x + 60.25 + x2 = 0 + 60.25 Reorder the terms: -60.25 + 60.25 + 2.25x + x2 = 0 + 60.25 Combine like terms: -60.25 + 60.25 = 0.00 0.00 + 2.25x + x2 = 0 + 60.25 2.25x + x2 = 0 + 60.25 Combine like terms: 0 + 60.25 = 60.25 2.25x + x2 = 60.25 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 = 60.25 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 60.25 + 1.265625 Combine like terms: 60.25 + 1.265625 = 61.515625 1.265625 + 2.25x + x2 = 61.515625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 61.515625 Calculate the square root of the right side: 7.843189721 Break this problem into two subproblems by setting (x + 1.125) equal to 7.843189721 and -7.843189721.Subproblem 1
x + 1.125 = 7.843189721 Simplifying x + 1.125 = 7.843189721 Reorder the terms: 1.125 + x = 7.843189721 Solving 1.125 + x = 7.843189721 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 = 7.843189721 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 7.843189721 + -1.125 x = 7.843189721 + -1.125 Combine like terms: 7.843189721 + -1.125 = 6.718189721 x = 6.718189721 Simplifying x = 6.718189721Subproblem 2
x + 1.125 = -7.843189721 Simplifying x + 1.125 = -7.843189721 Reorder the terms: 1.125 + x = -7.843189721 Solving 1.125 + x = -7.843189721 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 = -7.843189721 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -7.843189721 + -1.125 x = -7.843189721 + -1.125 Combine like terms: -7.843189721 + -1.125 = -8.968189721 x = -8.968189721 Simplifying x = -8.968189721Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.718189721, -8.968189721}
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