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Simplifying 5x2 + -5 * 0.707x + -0.2 = 0 Multiply -5 * 0.707 5x2 + -3.535x + -0.2 = 0 Reorder the terms: -0.2 + -3.535x + 5x2 = 0 Solving -0.2 + -3.535x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.04 + -0.707x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.707x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.707x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.707x + x2 = 0 + 0.04 -0.707x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.707x + x2 = 0.04 The x term is -0.707x. Take half its coefficient (-0.3535). Square it (0.12496225) and add it to both sides. Add '0.12496225' to each side of the equation. -0.707x + 0.12496225 + x2 = 0.04 + 0.12496225 Reorder the terms: 0.12496225 + -0.707x + x2 = 0.04 + 0.12496225 Combine like terms: 0.04 + 0.12496225 = 0.16496225 0.12496225 + -0.707x + x2 = 0.16496225 Factor a perfect square on the left side: (x + -0.3535)(x + -0.3535) = 0.16496225 Calculate the square root of the right side: 0.406155451 Break this problem into two subproblems by setting (x + -0.3535) equal to 0.406155451 and -0.406155451.Subproblem 1
x + -0.3535 = 0.406155451 Simplifying x + -0.3535 = 0.406155451 Reorder the terms: -0.3535 + x = 0.406155451 Solving -0.3535 + x = 0.406155451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3535' to each side of the equation. -0.3535 + 0.3535 + x = 0.406155451 + 0.3535 Combine like terms: -0.3535 + 0.3535 = 0.0000 0.0000 + x = 0.406155451 + 0.3535 x = 0.406155451 + 0.3535 Combine like terms: 0.406155451 + 0.3535 = 0.759655451 x = 0.759655451 Simplifying x = 0.759655451Subproblem 2
x + -0.3535 = -0.406155451 Simplifying x + -0.3535 = -0.406155451 Reorder the terms: -0.3535 + x = -0.406155451 Solving -0.3535 + x = -0.406155451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3535' to each side of the equation. -0.3535 + 0.3535 + x = -0.406155451 + 0.3535 Combine like terms: -0.3535 + 0.3535 = 0.0000 0.0000 + x = -0.406155451 + 0.3535 x = -0.406155451 + 0.3535 Combine like terms: -0.406155451 + 0.3535 = -0.052655451 x = -0.052655451 Simplifying x = -0.052655451Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.759655451, -0.052655451}
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