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Simplifying x(x) = 2x2 + 33x + -54 Multiply x * x x2 = 2x2 + 33x + -54 Reorder the terms: x2 = -54 + 33x + 2x2 Solving x2 = -54 + 33x + 2x2 Solving for variable 'x'. Reorder the terms: 54 + -33x + x2 + -2x2 = -54 + 33x + 2x2 + 54 + -33x + -2x2 Combine like terms: x2 + -2x2 = -1x2 54 + -33x + -1x2 = -54 + 33x + 2x2 + 54 + -33x + -2x2 Reorder the terms: 54 + -33x + -1x2 = -54 + 54 + 33x + -33x + 2x2 + -2x2 Combine like terms: -54 + 54 = 0 54 + -33x + -1x2 = 0 + 33x + -33x + 2x2 + -2x2 54 + -33x + -1x2 = 33x + -33x + 2x2 + -2x2 Combine like terms: 33x + -33x = 0 54 + -33x + -1x2 = 0 + 2x2 + -2x2 54 + -33x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 54 + -33x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 33x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 33x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 33x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 33x + x2 = 0 + 54 33x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 33x + x2 = 54 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = 54 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 54 + 272.25 Combine like terms: 54 + 272.25 = 326.25 272.25 + 33x + x2 = 326.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 326.25 Calculate the square root of the right side: 18.062391868 Break this problem into two subproblems by setting (x + 16.5) equal to 18.062391868 and -18.062391868.Subproblem 1
x + 16.5 = 18.062391868 Simplifying x + 16.5 = 18.062391868 Reorder the terms: 16.5 + x = 18.062391868 Solving 16.5 + x = 18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 18.062391868 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 18.062391868 + -16.5 x = 18.062391868 + -16.5 Combine like terms: 18.062391868 + -16.5 = 1.562391868 x = 1.562391868 Simplifying x = 1.562391868Subproblem 2
x + 16.5 = -18.062391868 Simplifying x + 16.5 = -18.062391868 Reorder the terms: 16.5 + x = -18.062391868 Solving 16.5 + x = -18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -18.062391868 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -18.062391868 + -16.5 x = -18.062391868 + -16.5 Combine like terms: -18.062391868 + -16.5 = -34.562391868 x = -34.562391868 Simplifying x = -34.562391868Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.562391868, -34.562391868}
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