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Simplifying 4x2 + -31x + -46 = 0 Reorder the terms: -46 + -31x + 4x2 = 0 Solving -46 + -31x + 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'. -11.5 + -7.75x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -7.75x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -7.75x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -7.75x + x2 = 0 + 11.5 -7.75x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -7.75x + x2 = 11.5 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = 11.5 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 11.5 + 15.015625 Combine like terms: 11.5 + 15.015625 = 26.515625 15.015625 + -7.75x + x2 = 26.515625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 26.515625 Calculate the square root of the right side: 5.149332481 Break this problem into two subproblems by setting (x + -3.875) equal to 5.149332481 and -5.149332481.Subproblem 1
x + -3.875 = 5.149332481 Simplifying x + -3.875 = 5.149332481 Reorder the terms: -3.875 + x = 5.149332481 Solving -3.875 + x = 5.149332481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 5.149332481 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 5.149332481 + 3.875 x = 5.149332481 + 3.875 Combine like terms: 5.149332481 + 3.875 = 9.024332481 x = 9.024332481 Simplifying x = 9.024332481Subproblem 2
x + -3.875 = -5.149332481 Simplifying x + -3.875 = -5.149332481 Reorder the terms: -3.875 + x = -5.149332481 Solving -3.875 + x = -5.149332481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -5.149332481 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -5.149332481 + 3.875 x = -5.149332481 + 3.875 Combine like terms: -5.149332481 + 3.875 = -1.274332481 x = -1.274332481 Simplifying x = -1.274332481Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.024332481, -1.274332481}
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