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Simplifying x + -0.5x2 + 0.42 = 0 Reorder the terms: 0.42 + x + -0.5x2 = 0 Solving 0.42 + x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -0.84 + -2x + x2 = 0 Move the constant term to the right: Add '0.84' to each side of the equation. -0.84 + -2x + 0.84 + x2 = 0 + 0.84 Reorder the terms: -0.84 + 0.84 + -2x + x2 = 0 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + -2x + x2 = 0 + 0.84 -2x + x2 = 0 + 0.84 Combine like terms: 0 + 0.84 = 0.84 -2x + x2 = 0.84 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. -2x + 0.25 + x2 = 0.84 + 0.25 Reorder the terms: 0.25 + -2x + x2 = 0.84 + 0.25 Combine like terms: 0.84 + 0.25 = 1.09 0.25 + -2x + x2 = 1.09 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (x + 0.5) equal to 1.044030651 and -1.044030651.Subproblem 1
x + 0.5 = 1.044030651 Simplifying x + 0.5 = 1.044030651 Reorder the terms: 0.5 + x = 1.044030651 Solving 0.5 + x = 1.044030651 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 = 1.044030651 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.044030651 + -0.5 x = 1.044030651 + -0.5 Combine like terms: 1.044030651 + -0.5 = 0.544030651 x = 0.544030651 Simplifying x = 0.544030651Subproblem 2
x + 0.5 = -1.044030651 Simplifying x + 0.5 = -1.044030651 Reorder the terms: 0.5 + x = -1.044030651 Solving 0.5 + x = -1.044030651 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 = -1.044030651 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.044030651 + -0.5 x = -1.044030651 + -0.5 Combine like terms: -1.044030651 + -0.5 = -1.544030651 x = -1.544030651 Simplifying x = -1.544030651Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.544030651, -1.544030651}
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