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Simplifying 0.054x2 + x + -0.4 = 0 Reorder the terms: -0.4 + x + 0.054x2 = 0 Solving -0.4 + x + 0.054x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.054 the coefficient of the squared term: Divide each side by '0.054'. -7.407407407 + 18.51851852x + x2 = 0 Move the constant term to the right: Add '7.407407407' to each side of the equation. -7.407407407 + 18.51851852x + 7.407407407 + x2 = 0 + 7.407407407 Reorder the terms: -7.407407407 + 7.407407407 + 18.51851852x + x2 = 0 + 7.407407407 Combine like terms: -7.407407407 + 7.407407407 = 0.000000000 0.000000000 + 18.51851852x + x2 = 0 + 7.407407407 18.51851852x + x2 = 0 + 7.407407407 Combine like terms: 0 + 7.407407407 = 7.407407407 18.51851852x + x2 = 7.407407407 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 18.51851852x + 0.25 + x2 = 7.407407407 + 0.25 Reorder the terms: 0.25 + 18.51851852x + x2 = 7.407407407 + 0.25 Combine like terms: 7.407407407 + 0.25 = 7.657407407 0.25 + 18.51851852x + x2 = 7.657407407 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.657407407 Calculate the square root of the right side: 2.76720209 Break this problem into two subproblems by setting (x + 0.5) equal to 2.76720209 and -2.76720209.Subproblem 1
x + 0.5 = 2.76720209 Simplifying x + 0.5 = 2.76720209 Reorder the terms: 0.5 + x = 2.76720209 Solving 0.5 + x = 2.76720209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.76720209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.76720209 + -0.5 x = 2.76720209 + -0.5 Combine like terms: 2.76720209 + -0.5 = 2.26720209 x = 2.26720209 Simplifying x = 2.26720209Subproblem 2
x + 0.5 = -2.76720209 Simplifying x + 0.5 = -2.76720209 Reorder the terms: 0.5 + x = -2.76720209 Solving 0.5 + x = -2.76720209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.76720209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.76720209 + -0.5 x = -2.76720209 + -0.5 Combine like terms: -2.76720209 + -0.5 = -3.26720209 x = -3.26720209 Simplifying x = -3.26720209Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.26720209, -3.26720209}
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