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Simplifying 0.2 = 0.5x(10 + x) 0.2 = (10 * 0.5x + x * 0.5x) 0.2 = (5x + 0.5x2) Solving 0.2 = 5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 0.2 + -5x + -0.5x2 = 5x + -5x + 0.5x2 + -0.5x2 Combine like terms: 5x + -5x = 0 0.2 + -5x + -0.5x2 = 0 + 0.5x2 + -0.5x2 0.2 + -5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 0.2 + -5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -0.4 + 10x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 10x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 10x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 10x + x2 = 0 + 0.4 10x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 10x + x2 = 0.4 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 0.4 + 25 Reorder the terms: 25 + 10x + x2 = 0.4 + 25 Combine like terms: 0.4 + 25 = 25.4 25 + 10x + x2 = 25.4 Factor a perfect square on the left side: (x + 5)(x + 5) = 25.4 Calculate the square root of the right side: 5.039841267 Break this problem into two subproblems by setting (x + 5) equal to 5.039841267 and -5.039841267.Subproblem 1
x + 5 = 5.039841267 Simplifying x + 5 = 5.039841267 Reorder the terms: 5 + x = 5.039841267 Solving 5 + x = 5.039841267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.039841267 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.039841267 + -5 x = 5.039841267 + -5 Combine like terms: 5.039841267 + -5 = 0.039841267 x = 0.039841267 Simplifying x = 0.039841267Subproblem 2
x + 5 = -5.039841267 Simplifying x + 5 = -5.039841267 Reorder the terms: 5 + x = -5.039841267 Solving 5 + x = -5.039841267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.039841267 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.039841267 + -5 x = -5.039841267 + -5 Combine like terms: -5.039841267 + -5 = -10.039841267 x = -10.039841267 Simplifying x = -10.039841267Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039841267, -10.039841267}
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