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Simplifying (x2 + 5x + -24) = (-1x2 + -4x + 9) Reorder the terms: (-24 + 5x + x2) = (-1x2 + -4x + 9) Remove parenthesis around (-24 + 5x + x2) -24 + 5x + x2 = (-1x2 + -4x + 9) Reorder the terms: -24 + 5x + x2 = (9 + -4x + -1x2) Remove parenthesis around (9 + -4x + -1x2) -24 + 5x + x2 = 9 + -4x + -1x2 Solving -24 + 5x + x2 = 9 + -4x + -1x2 Solving for variable 'x'. Reorder the terms: -24 + -9 + 5x + 4x + x2 + x2 = 9 + -4x + -1x2 + -9 + 4x + x2 Combine like terms: -24 + -9 = -33 -33 + 5x + 4x + x2 + x2 = 9 + -4x + -1x2 + -9 + 4x + x2 Combine like terms: 5x + 4x = 9x -33 + 9x + x2 + x2 = 9 + -4x + -1x2 + -9 + 4x + x2 Combine like terms: x2 + x2 = 2x2 -33 + 9x + 2x2 = 9 + -4x + -1x2 + -9 + 4x + x2 Reorder the terms: -33 + 9x + 2x2 = 9 + -9 + -4x + 4x + -1x2 + x2 Combine like terms: 9 + -9 = 0 -33 + 9x + 2x2 = 0 + -4x + 4x + -1x2 + x2 -33 + 9x + 2x2 = -4x + 4x + -1x2 + x2 Combine like terms: -4x + 4x = 0 -33 + 9x + 2x2 = 0 + -1x2 + x2 -33 + 9x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -33 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 4.5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 4.5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 4.5x + x2 = 0 + 16.5 4.5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 4.5x + x2 = 16.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 16.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 16.5 + 5.0625 Combine like terms: 16.5 + 5.0625 = 21.5625 5.0625 + 4.5x + x2 = 21.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 21.5625 Calculate the square root of the right side: 4.643543905 Break this problem into two subproblems by setting (x + 2.25) equal to 4.643543905 and -4.643543905.Subproblem 1
x + 2.25 = 4.643543905 Simplifying x + 2.25 = 4.643543905 Reorder the terms: 2.25 + x = 4.643543905 Solving 2.25 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.643543905 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.643543905 + -2.25 x = 4.643543905 + -2.25 Combine like terms: 4.643543905 + -2.25 = 2.393543905 x = 2.393543905 Simplifying x = 2.393543905Subproblem 2
x + 2.25 = -4.643543905 Simplifying x + 2.25 = -4.643543905 Reorder the terms: 2.25 + x = -4.643543905 Solving 2.25 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.643543905 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.643543905 + -2.25 x = -4.643543905 + -2.25 Combine like terms: -4.643543905 + -2.25 = -6.893543905 x = -6.893543905 Simplifying x = -6.893543905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.393543905, -6.893543905}
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