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Simplifying 2x2 + x + -42.2 = 0 Reorder the terms: -42.2 + x + 2x2 = 0 Solving -42.2 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.1 + 0.5x + x2 = 0 Move the constant term to the right: Add '21.1' to each side of the equation. -21.1 + 0.5x + 21.1 + x2 = 0 + 21.1 Reorder the terms: -21.1 + 21.1 + 0.5x + x2 = 0 + 21.1 Combine like terms: -21.1 + 21.1 = 0.0 0.0 + 0.5x + x2 = 0 + 21.1 0.5x + x2 = 0 + 21.1 Combine like terms: 0 + 21.1 = 21.1 0.5x + x2 = 21.1 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. 0.5x + 0.25 + x2 = 21.1 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 21.1 + 0.25 Combine like terms: 21.1 + 0.25 = 21.35 0.25 + 0.5x + x2 = 21.35 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.35 Calculate the square root of the right side: 4.620606021 Break this problem into two subproblems by setting (x + 0.5) equal to 4.620606021 and -4.620606021.Subproblem 1
x + 0.5 = 4.620606021 Simplifying x + 0.5 = 4.620606021 Reorder the terms: 0.5 + x = 4.620606021 Solving 0.5 + x = 4.620606021 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 = 4.620606021 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.620606021 + -0.5 x = 4.620606021 + -0.5 Combine like terms: 4.620606021 + -0.5 = 4.120606021 x = 4.120606021 Simplifying x = 4.120606021Subproblem 2
x + 0.5 = -4.620606021 Simplifying x + 0.5 = -4.620606021 Reorder the terms: 0.5 + x = -4.620606021 Solving 0.5 + x = -4.620606021 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 = -4.620606021 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.620606021 + -0.5 x = -4.620606021 + -0.5 Combine like terms: -4.620606021 + -0.5 = -5.120606021 x = -5.120606021 Simplifying x = -5.120606021Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.120606021, -5.120606021}
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