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Simplifying x2 + -2.33x + 0.67 = 0 Reorder the terms: 0.67 + -2.33x + x2 = 0 Solving 0.67 + -2.33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.67' to each side of the equation. 0.67 + -2.33x + -0.67 + x2 = 0 + -0.67 Reorder the terms: 0.67 + -0.67 + -2.33x + x2 = 0 + -0.67 Combine like terms: 0.67 + -0.67 = 0.00 0.00 + -2.33x + x2 = 0 + -0.67 -2.33x + x2 = 0 + -0.67 Combine like terms: 0 + -0.67 = -0.67 -2.33x + x2 = -0.67 The x term is -2.33x. Take half its coefficient (-1.165). Square it (1.357225) and add it to both sides. Add '1.357225' to each side of the equation. -2.33x + 1.357225 + x2 = -0.67 + 1.357225 Reorder the terms: 1.357225 + -2.33x + x2 = -0.67 + 1.357225 Combine like terms: -0.67 + 1.357225 = 0.687225 1.357225 + -2.33x + x2 = 0.687225 Factor a perfect square on the left side: (x + -1.165)(x + -1.165) = 0.687225 Calculate the square root of the right side: 0.82899035 Break this problem into two subproblems by setting (x + -1.165) equal to 0.82899035 and -0.82899035.Subproblem 1
x + -1.165 = 0.82899035 Simplifying x + -1.165 = 0.82899035 Reorder the terms: -1.165 + x = 0.82899035 Solving -1.165 + x = 0.82899035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.165' to each side of the equation. -1.165 + 1.165 + x = 0.82899035 + 1.165 Combine like terms: -1.165 + 1.165 = 0.000 0.000 + x = 0.82899035 + 1.165 x = 0.82899035 + 1.165 Combine like terms: 0.82899035 + 1.165 = 1.99399035 x = 1.99399035 Simplifying x = 1.99399035Subproblem 2
x + -1.165 = -0.82899035 Simplifying x + -1.165 = -0.82899035 Reorder the terms: -1.165 + x = -0.82899035 Solving -1.165 + x = -0.82899035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.165' to each side of the equation. -1.165 + 1.165 + x = -0.82899035 + 1.165 Combine like terms: -1.165 + 1.165 = 0.000 0.000 + x = -0.82899035 + 1.165 x = -0.82899035 + 1.165 Combine like terms: -0.82899035 + 1.165 = 0.33600965 x = 0.33600965 Simplifying x = 0.33600965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.99399035, 0.33600965}
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