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Simplifying 3x2 + -24x + -48 = 7 Reorder the terms: -48 + -24x + 3x2 = 7 Solving -48 + -24x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: -48 + -7 + -24x + 3x2 = 7 + -7 Combine like terms: -48 + -7 = -55 -55 + -24x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -55 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '18.33333333' to each side of the equation. -18.33333333 + -8x + 18.33333333 + x2 = 0 + 18.33333333 Reorder the terms: -18.33333333 + 18.33333333 + -8x + x2 = 0 + 18.33333333 Combine like terms: -18.33333333 + 18.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + 18.33333333 -8x + x2 = 0 + 18.33333333 Combine like terms: 0 + 18.33333333 = 18.33333333 -8x + x2 = 18.33333333 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 = 18.33333333 + 16 Reorder the terms: 16 + -8x + x2 = 18.33333333 + 16 Combine like terms: 18.33333333 + 16 = 34.33333333 16 + -8x + x2 = 34.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 34.33333333 Calculate the square root of the right side: 5.859465277 Break this problem into two subproblems by setting (x + -4) equal to 5.859465277 and -5.859465277.Subproblem 1
x + -4 = 5.859465277 Simplifying x + -4 = 5.859465277 Reorder the terms: -4 + x = 5.859465277 Solving -4 + x = 5.859465277 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 = 5.859465277 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.859465277 + 4 x = 5.859465277 + 4 Combine like terms: 5.859465277 + 4 = 9.859465277 x = 9.859465277 Simplifying x = 9.859465277Subproblem 2
x + -4 = -5.859465277 Simplifying x + -4 = -5.859465277 Reorder the terms: -4 + x = -5.859465277 Solving -4 + x = -5.859465277 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 = -5.859465277 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.859465277 + 4 x = -5.859465277 + 4 Combine like terms: -5.859465277 + 4 = -1.859465277 x = -1.859465277 Simplifying x = -1.859465277Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.859465277, -1.859465277}
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