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Simplifying x2 + -3.1x + 0.42 = 0 Reorder the terms: 0.42 + -3.1x + x2 = 0 Solving 0.42 + -3.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.42' to each side of the equation. 0.42 + -3.1x + -0.42 + x2 = 0 + -0.42 Reorder the terms: 0.42 + -0.42 + -3.1x + x2 = 0 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + -3.1x + x2 = 0 + -0.42 -3.1x + x2 = 0 + -0.42 Combine like terms: 0 + -0.42 = -0.42 -3.1x + x2 = -0.42 The x term is -3.1x. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1x + 2.4025 + x2 = -0.42 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = -0.42 + 2.4025 Combine like terms: -0.42 + 2.4025 = 1.9825 2.4025 + -3.1x + x2 = 1.9825 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 1.9825 Calculate the square root of the right side: 1.408012784 Break this problem into two subproblems by setting (x + -1.55) equal to 1.408012784 and -1.408012784.Subproblem 1
x + -1.55 = 1.408012784 Simplifying x + -1.55 = 1.408012784 Reorder the terms: -1.55 + x = 1.408012784 Solving -1.55 + x = 1.408012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = 1.408012784 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 1.408012784 + 1.55 x = 1.408012784 + 1.55 Combine like terms: 1.408012784 + 1.55 = 2.958012784 x = 2.958012784 Simplifying x = 2.958012784Subproblem 2
x + -1.55 = -1.408012784 Simplifying x + -1.55 = -1.408012784 Reorder the terms: -1.55 + x = -1.408012784 Solving -1.55 + x = -1.408012784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = -1.408012784 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -1.408012784 + 1.55 x = -1.408012784 + 1.55 Combine like terms: -1.408012784 + 1.55 = 0.141987216 x = 0.141987216 Simplifying x = 0.141987216Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.958012784, 0.141987216}
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