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Simplifying 4x2 + -29x + -39 = 0 Reorder the terms: -39 + -29x + 4x2 = 0 Solving -39 + -29x + 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'. -9.75 + -7.25x + x2 = 0 Move the constant term to the right: Add '9.75' to each side of the equation. -9.75 + -7.25x + 9.75 + x2 = 0 + 9.75 Reorder the terms: -9.75 + 9.75 + -7.25x + x2 = 0 + 9.75 Combine like terms: -9.75 + 9.75 = 0.00 0.00 + -7.25x + x2 = 0 + 9.75 -7.25x + x2 = 0 + 9.75 Combine like terms: 0 + 9.75 = 9.75 -7.25x + x2 = 9.75 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 9.75 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 9.75 + 13.140625 Combine like terms: 9.75 + 13.140625 = 22.890625 13.140625 + -7.25x + x2 = 22.890625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 22.890625 Calculate the square root of the right side: 4.784414802 Break this problem into two subproblems by setting (x + -3.625) equal to 4.784414802 and -4.784414802.Subproblem 1
x + -3.625 = 4.784414802 Simplifying x + -3.625 = 4.784414802 Reorder the terms: -3.625 + x = 4.784414802 Solving -3.625 + x = 4.784414802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 4.784414802 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 4.784414802 + 3.625 x = 4.784414802 + 3.625 Combine like terms: 4.784414802 + 3.625 = 8.409414802 x = 8.409414802 Simplifying x = 8.409414802Subproblem 2
x + -3.625 = -4.784414802 Simplifying x + -3.625 = -4.784414802 Reorder the terms: -3.625 + x = -4.784414802 Solving -3.625 + x = -4.784414802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -4.784414802 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -4.784414802 + 3.625 x = -4.784414802 + 3.625 Combine like terms: -4.784414802 + 3.625 = -1.159414802 x = -1.159414802 Simplifying x = -1.159414802Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.409414802, -1.159414802}
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