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Simplifying x2 + 2.333x + -3 = 0 Reorder the terms: -3 + 2.333x + x2 = 0 Solving -3 + 2.333x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.333x + x2 = 0 + 3 2.333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.333x + x2 = 3 The x term is 2.333x. Take half its coefficient (1.1665). Square it (1.36072225) and add it to both sides. Add '1.36072225' to each side of the equation. 2.333x + 1.36072225 + x2 = 3 + 1.36072225 Reorder the terms: 1.36072225 + 2.333x + x2 = 3 + 1.36072225 Combine like terms: 3 + 1.36072225 = 4.36072225 1.36072225 + 2.333x + x2 = 4.36072225 Factor a perfect square on the left side: (x + 1.1665)(x + 1.1665) = 4.36072225 Calculate the square root of the right side: 2.088234242 Break this problem into two subproblems by setting (x + 1.1665) equal to 2.088234242 and -2.088234242.Subproblem 1
x + 1.1665 = 2.088234242 Simplifying x + 1.1665 = 2.088234242 Reorder the terms: 1.1665 + x = 2.088234242 Solving 1.1665 + x = 2.088234242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1665' to each side of the equation. 1.1665 + -1.1665 + x = 2.088234242 + -1.1665 Combine like terms: 1.1665 + -1.1665 = 0.0000 0.0000 + x = 2.088234242 + -1.1665 x = 2.088234242 + -1.1665 Combine like terms: 2.088234242 + -1.1665 = 0.921734242 x = 0.921734242 Simplifying x = 0.921734242Subproblem 2
x + 1.1665 = -2.088234242 Simplifying x + 1.1665 = -2.088234242 Reorder the terms: 1.1665 + x = -2.088234242 Solving 1.1665 + x = -2.088234242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1665' to each side of the equation. 1.1665 + -1.1665 + x = -2.088234242 + -1.1665 Combine like terms: 1.1665 + -1.1665 = 0.0000 0.0000 + x = -2.088234242 + -1.1665 x = -2.088234242 + -1.1665 Combine like terms: -2.088234242 + -1.1665 = -3.254734242 x = -3.254734242 Simplifying x = -3.254734242Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.921734242, -3.254734242}
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