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Simplifying 3x2 + -24x + 38 = 3.5 Reorder the terms: 38 + -24x + 3x2 = 3.5 Solving 38 + -24x + 3x2 = 3.5 Solving for variable 'x'. Reorder the terms: 38 + -3.5 + -24x + 3x2 = 3.5 + -3.5 Combine like terms: 38 + -3.5 = 34.5 34.5 + -24x + 3x2 = 3.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 34.5 + -24x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 11.5 + -8x + x2 = 0.0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -8x + -11.5 + x2 = 0.0 + -11.5 Reorder the terms: 11.5 + -11.5 + -8x + x2 = 0.0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -8x + x2 = 0.0 + -11.5 -8x + x2 = 0.0 + -11.5 Combine like terms: 0.0 + -11.5 = -11.5 -8x + x2 = -11.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11.5 + 16 Reorder the terms: 16 + -8x + x2 = -11.5 + 16 Combine like terms: -11.5 + 16 = 4.5 16 + -8x + x2 = 4.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -4) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -4 = 2.121320344 Simplifying x + -4 = 2.121320344 Reorder the terms: -4 + x = 2.121320344 Solving -4 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.121320344 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.121320344 + 4 x = 2.121320344 + 4 Combine like terms: 2.121320344 + 4 = 6.121320344 x = 6.121320344 Simplifying x = 6.121320344Subproblem 2
x + -4 = -2.121320344 Simplifying x + -4 = -2.121320344 Reorder the terms: -4 + x = -2.121320344 Solving -4 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.121320344 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.121320344 + 4 x = -2.121320344 + 4 Combine like terms: -2.121320344 + 4 = 1.878679656 x = 1.878679656 Simplifying x = 1.878679656Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.121320344, 1.878679656}
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