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Simplifying 4x2 + -29x + 33 = 0 Reorder the terms: 33 + -29x + 4x2 = 0 Solving 33 + -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'. 8.25 + -7.25x + x2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -7.25x + -8.25 + x2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -7.25x + x2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -7.25x + x2 = 0 + -8.25 -7.25x + x2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -7.25x + x2 = -8.25 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 = -8.25 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -8.25 + 13.140625 Combine like terms: -8.25 + 13.140625 = 4.890625 13.140625 + -7.25x + x2 = 4.890625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + -3.625) equal to 2.211475752 and -2.211475752.Subproblem 1
x + -3.625 = 2.211475752 Simplifying x + -3.625 = 2.211475752 Reorder the terms: -3.625 + x = 2.211475752 Solving -3.625 + x = 2.211475752 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 = 2.211475752 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 2.211475752 + 3.625 x = 2.211475752 + 3.625 Combine like terms: 2.211475752 + 3.625 = 5.836475752 x = 5.836475752 Simplifying x = 5.836475752Subproblem 2
x + -3.625 = -2.211475752 Simplifying x + -3.625 = -2.211475752 Reorder the terms: -3.625 + x = -2.211475752 Solving -3.625 + x = -2.211475752 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 = -2.211475752 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -2.211475752 + 3.625 x = -2.211475752 + 3.625 Combine like terms: -2.211475752 + 3.625 = 1.413524248 x = 1.413524248 Simplifying x = 1.413524248Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.836475752, 1.413524248}
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