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Simplifying 3x2 + -41 = -4x2 + -7x + -24 Reorder the terms: -41 + 3x2 = -4x2 + -7x + -24 Reorder the terms: -41 + 3x2 = -24 + -7x + -4x2 Solving -41 + 3x2 = -24 + -7x + -4x2 Solving for variable 'x'. Reorder the terms: -41 + 24 + 7x + 3x2 + 4x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2 Combine like terms: -41 + 24 = -17 -17 + 7x + 3x2 + 4x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2 Combine like terms: 3x2 + 4x2 = 7x2 -17 + 7x + 7x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2 Reorder the terms: -17 + 7x + 7x2 = -24 + 24 + -7x + 7x + -4x2 + 4x2 Combine like terms: -24 + 24 = 0 -17 + 7x + 7x2 = 0 + -7x + 7x + -4x2 + 4x2 -17 + 7x + 7x2 = -7x + 7x + -4x2 + 4x2 Combine like terms: -7x + 7x = 0 -17 + 7x + 7x2 = 0 + -4x2 + 4x2 -17 + 7x + 7x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -17 + 7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.428571429 + x + x2 = 0 Move the constant term to the right: Add '2.428571429' to each side of the equation. -2.428571429 + x + 2.428571429 + x2 = 0 + 2.428571429 Reorder the terms: -2.428571429 + 2.428571429 + x + x2 = 0 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x + x2 = 0 + 2.428571429 x + x2 = 0 + 2.428571429 Combine like terms: 0 + 2.428571429 = 2.428571429 x + x2 = 2.428571429 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.428571429 + 0.25 Combine like terms: 2.428571429 + 0.25 = 2.678571429 1.25 + x2 = 2.678571429 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.678571429 Calculate the square root of the right side: 1.636634177 Break this problem into two subproblems by setting (x + 0.5) equal to 1.636634177 and -1.636634177.Subproblem 1
x + 0.5 = 1.636634177 Simplifying x + 0.5 = 1.636634177 Reorder the terms: 0.5 + x = 1.636634177 Solving 0.5 + x = 1.636634177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.636634177 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.636634177 + -0.5 x = 1.636634177 + -0.5 Combine like terms: 1.636634177 + -0.5 = 1.136634177 x = 1.136634177 Simplifying x = 1.136634177Subproblem 2
x + 0.5 = -1.636634177 Simplifying x + 0.5 = -1.636634177 Reorder the terms: 0.5 + x = -1.636634177 Solving 0.5 + x = -1.636634177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.636634177 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.636634177 + -0.5 x = -1.636634177 + -0.5 Combine like terms: -1.636634177 + -0.5 = -2.136634177 x = -2.136634177 Simplifying x = -2.136634177Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.136634177, -2.136634177}
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