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Simplifying x2 + 3x + -54 = 44 Reorder the terms: -54 + 3x + x2 = 44 Solving -54 + 3x + x2 = 44 Solving for variable 'x'. Reorder the terms: -54 + -44 + 3x + x2 = 44 + -44 Combine like terms: -54 + -44 = -98 -98 + 3x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -98 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 3x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 3x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 3x + x2 = 0 + 98 3x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 3x + x2 = 98 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 = 98 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 98 + 2.25 Combine like terms: 98 + 2.25 = 100.25 2.25 + 3x + x2 = 100.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 1.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 1.5 = 10.012492197 Simplifying x + 1.5 = 10.012492197 Reorder the terms: 1.5 + x = 10.012492197 Solving 1.5 + x = 10.012492197 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 = 10.012492197 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.012492197 + -1.5 x = 10.012492197 + -1.5 Combine like terms: 10.012492197 + -1.5 = 8.512492197 x = 8.512492197 Simplifying x = 8.512492197Subproblem 2
x + 1.5 = -10.012492197 Simplifying x + 1.5 = -10.012492197 Reorder the terms: 1.5 + x = -10.012492197 Solving 1.5 + x = -10.012492197 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 = -10.012492197 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.012492197 + -1.5 x = -10.012492197 + -1.5 Combine like terms: -10.012492197 + -1.5 = -11.512492197 x = -11.512492197 Simplifying x = -11.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.512492197, -11.512492197}
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