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Simplifying x2 + 3x = 927 Reorder the terms: 3x + x2 = 927 Solving 3x + x2 = 927 Solving for variable 'x'. Reorder the terms: -927 + 3x + x2 = 927 + -927 Combine like terms: 927 + -927 = 0 -927 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '927' to each side of the equation. -927 + 3x + 927 + x2 = 0 + 927 Reorder the terms: -927 + 927 + 3x + x2 = 0 + 927 Combine like terms: -927 + 927 = 0 0 + 3x + x2 = 0 + 927 3x + x2 = 0 + 927 Combine like terms: 0 + 927 = 927 3x + x2 = 927 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 = 927 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 927 + 2.25 Combine like terms: 927 + 2.25 = 929.25 2.25 + 3x + x2 = 929.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 929.25 Calculate the square root of the right side: 30.483602149 Break this problem into two subproblems by setting (x + 1.5) equal to 30.483602149 and -30.483602149.Subproblem 1
x + 1.5 = 30.483602149 Simplifying x + 1.5 = 30.483602149 Reorder the terms: 1.5 + x = 30.483602149 Solving 1.5 + x = 30.483602149 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 = 30.483602149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 30.483602149 + -1.5 x = 30.483602149 + -1.5 Combine like terms: 30.483602149 + -1.5 = 28.983602149 x = 28.983602149 Simplifying x = 28.983602149Subproblem 2
x + 1.5 = -30.483602149 Simplifying x + 1.5 = -30.483602149 Reorder the terms: 1.5 + x = -30.483602149 Solving 1.5 + x = -30.483602149 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 = -30.483602149 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -30.483602149 + -1.5 x = -30.483602149 + -1.5 Combine like terms: -30.483602149 + -1.5 = -31.983602149 x = -31.983602149 Simplifying x = -31.983602149Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.983602149, -31.983602149}
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