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Simplifying x(x + 3) = 1083 Reorder the terms: x(3 + x) = 1083 (3 * x + x * x) = 1083 (3x + x2) = 1083 Solving 3x + x2 = 1083 Solving for variable 'x'. Reorder the terms: -1083 + 3x + x2 = 1083 + -1083 Combine like terms: 1083 + -1083 = 0 -1083 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1083' to each side of the equation. -1083 + 3x + 1083 + x2 = 0 + 1083 Reorder the terms: -1083 + 1083 + 3x + x2 = 0 + 1083 Combine like terms: -1083 + 1083 = 0 0 + 3x + x2 = 0 + 1083 3x + x2 = 0 + 1083 Combine like terms: 0 + 1083 = 1083 3x + x2 = 1083 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 = 1083 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1083 + 2.25 Combine like terms: 1083 + 2.25 = 1085.25 2.25 + 3x + x2 = 1085.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1085.25 Calculate the square root of the right side: 32.94313282 Break this problem into two subproblems by setting (x + 1.5) equal to 32.94313282 and -32.94313282.Subproblem 1
x + 1.5 = 32.94313282 Simplifying x + 1.5 = 32.94313282 Reorder the terms: 1.5 + x = 32.94313282 Solving 1.5 + x = 32.94313282 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 = 32.94313282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 32.94313282 + -1.5 x = 32.94313282 + -1.5 Combine like terms: 32.94313282 + -1.5 = 31.44313282 x = 31.44313282 Simplifying x = 31.44313282Subproblem 2
x + 1.5 = -32.94313282 Simplifying x + 1.5 = -32.94313282 Reorder the terms: 1.5 + x = -32.94313282 Solving 1.5 + x = -32.94313282 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 = -32.94313282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -32.94313282 + -1.5 x = -32.94313282 + -1.5 Combine like terms: -32.94313282 + -1.5 = -34.44313282 x = -34.44313282 Simplifying x = -34.44313282Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.44313282, -34.44313282}
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