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Simplifying 0 = 2 + -8x + -5x2 Solving 0 = 2 + -8x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + 8x + 5x2 = 2 + -8x + -5x2 + -2 + 8x + 5x2 Reorder the terms: -2 + 8x + 5x2 = 2 + -2 + -8x + 8x + -5x2 + 5x2 Combine like terms: 2 + -2 = 0 -2 + 8x + 5x2 = 0 + -8x + 8x + -5x2 + 5x2 -2 + 8x + 5x2 = -8x + 8x + -5x2 + 5x2 Combine like terms: -8x + 8x = 0 -2 + 8x + 5x2 = 0 + -5x2 + 5x2 -2 + 8x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -2 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 1.6x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.6x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.6x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.6x + x2 = 0 + 0.4 1.6x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.6x + x2 = 0.4 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 0.4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 0.4 + 0.64 Combine like terms: 0.4 + 0.64 = 1.04 0.64 + 1.6x + x2 = 1.04 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + 0.8) equal to 1.019803903 and -1.019803903.Subproblem 1
x + 0.8 = 1.019803903 Simplifying x + 0.8 = 1.019803903 Reorder the terms: 0.8 + x = 1.019803903 Solving 0.8 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.019803903 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.019803903 + -0.8 x = 1.019803903 + -0.8 Combine like terms: 1.019803903 + -0.8 = 0.219803903 x = 0.219803903 Simplifying x = 0.219803903Subproblem 2
x + 0.8 = -1.019803903 Simplifying x + 0.8 = -1.019803903 Reorder the terms: 0.8 + x = -1.019803903 Solving 0.8 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.019803903 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.019803903 + -0.8 x = -1.019803903 + -0.8 Combine like terms: -1.019803903 + -0.8 = -1.819803903 x = -1.819803903 Simplifying x = -1.819803903Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.219803903, -1.819803903}
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