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Simplifying x2 + 3x + -54 = 33 Reorder the terms: -54 + 3x + x2 = 33 Solving -54 + 3x + x2 = 33 Solving for variable 'x'. Reorder the terms: -54 + -33 + 3x + x2 = 33 + -33 Combine like terms: -54 + -33 = -87 -87 + 3x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -87 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 3x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 3x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 3x + x2 = 0 + 87 3x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 3x + x2 = 87 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 87 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 87 + 2.25 Combine like terms: 87 + 2.25 = 89.25 2.25 + 3x + x2 = 89.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + 1.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + 1.5 = 9.447221814 Simplifying x + 1.5 = 9.447221814 Reorder the terms: 1.5 + x = 9.447221814 Solving 1.5 + x = 9.447221814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.447221814 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.447221814 + -1.5 x = 9.447221814 + -1.5 Combine like terms: 9.447221814 + -1.5 = 7.947221814 x = 7.947221814 Simplifying x = 7.947221814Subproblem 2
x + 1.5 = -9.447221814 Simplifying x + 1.5 = -9.447221814 Reorder the terms: 1.5 + x = -9.447221814 Solving 1.5 + x = -9.447221814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.447221814 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.447221814 + -1.5 x = -9.447221814 + -1.5 Combine like terms: -9.447221814 + -1.5 = -10.947221814 x = -10.947221814 Simplifying x = -10.947221814Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.947221814, -10.947221814}
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