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Simplifying x2 + 2.76x + -0.33 = 0 Reorder the terms: -0.33 + 2.76x + x2 = 0 Solving -0.33 + 2.76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.33' to each side of the equation. -0.33 + 2.76x + 0.33 + x2 = 0 + 0.33 Reorder the terms: -0.33 + 0.33 + 2.76x + x2 = 0 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + 2.76x + x2 = 0 + 0.33 2.76x + x2 = 0 + 0.33 Combine like terms: 0 + 0.33 = 0.33 2.76x + x2 = 0.33 The x term is 2.76x. Take half its coefficient (1.38). Square it (1.9044) and add it to both sides. Add '1.9044' to each side of the equation. 2.76x + 1.9044 + x2 = 0.33 + 1.9044 Reorder the terms: 1.9044 + 2.76x + x2 = 0.33 + 1.9044 Combine like terms: 0.33 + 1.9044 = 2.2344 1.9044 + 2.76x + x2 = 2.2344 Factor a perfect square on the left side: (x + 1.38)(x + 1.38) = 2.2344 Calculate the square root of the right side: 1.494790955 Break this problem into two subproblems by setting (x + 1.38) equal to 1.494790955 and -1.494790955.Subproblem 1
x + 1.38 = 1.494790955 Simplifying x + 1.38 = 1.494790955 Reorder the terms: 1.38 + x = 1.494790955 Solving 1.38 + x = 1.494790955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.38' to each side of the equation. 1.38 + -1.38 + x = 1.494790955 + -1.38 Combine like terms: 1.38 + -1.38 = 0.00 0.00 + x = 1.494790955 + -1.38 x = 1.494790955 + -1.38 Combine like terms: 1.494790955 + -1.38 = 0.114790955 x = 0.114790955 Simplifying x = 0.114790955Subproblem 2
x + 1.38 = -1.494790955 Simplifying x + 1.38 = -1.494790955 Reorder the terms: 1.38 + x = -1.494790955 Solving 1.38 + x = -1.494790955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.38' to each side of the equation. 1.38 + -1.38 + x = -1.494790955 + -1.38 Combine like terms: 1.38 + -1.38 = 0.00 0.00 + x = -1.494790955 + -1.38 x = -1.494790955 + -1.38 Combine like terms: -1.494790955 + -1.38 = -2.874790955 x = -2.874790955 Simplifying x = -2.874790955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.114790955, -2.874790955}
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