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Simplifying x(0.1x + -1) = 0.00000014 Reorder the terms: x(-1 + 0.1x) = 0.00000014 (-1 * x + 0.1x * x) = 0.00000014 (-1x + 0.1x2) = 0.00000014 Solving -1x + 0.1x2 = 0.00000014 Solving for variable 'x'. Reorder the terms: -0.00000014 + -1x + 0.1x2 = 0.00000014 + -0.00000014 Combine like terms: 0.00000014 + -0.00000014 = 0.00000000 -0.00000014 + -1x + 0.1x2 = 0.00000000 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -0.0000014 + -10x + x2 = 0.0000000 Move the constant term to the right: Add '0.0000014' to each side of the equation. -0.0000014 + -10x + 0.0000014 + x2 = 0.0000000 + 0.0000014 Reorder the terms: -0.0000014 + 0.0000014 + -10x + x2 = 0.0000000 + 0.0000014 Combine like terms: -0.0000014 + 0.0000014 = 0.0000000 0.0000000 + -10x + x2 = 0.0000000 + 0.0000014 -10x + x2 = 0.0000000 + 0.0000014 Combine like terms: 0.0000000 + 0.0000014 = 0.0000014 -10x + x2 = 0.0000014 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 = 0.0000014 + 25 Reorder the terms: 25 + -10x + x2 = 0.0000014 + 25 Combine like terms: 0.0000014 + 25 = 25.0000014 25 + -10x + x2 = 25.0000014 Factor a perfect square on the left side: (x + -5)(x + -5) = 25.0000014 Calculate the square root of the right side: 5.00000014 Break this problem into two subproblems by setting (x + -5) equal to 5.00000014 and -5.00000014.Subproblem 1
x + -5 = 5.00000014 Simplifying x + -5 = 5.00000014 Reorder the terms: -5 + x = 5.00000014 Solving -5 + x = 5.00000014 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 = 5.00000014 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.00000014 + 5 x = 5.00000014 + 5 Combine like terms: 5.00000014 + 5 = 10.00000014 x = 10.00000014 Simplifying x = 10.00000014Subproblem 2
x + -5 = -5.00000014 Simplifying x + -5 = -5.00000014 Reorder the terms: -5 + x = -5.00000014 Solving -5 + x = -5.00000014 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 = -5.00000014 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.00000014 + 5 x = -5.00000014 + 5 Combine like terms: -5.00000014 + 5 = -0.00000014 x = -0.00000014 Simplifying x = -0.00000014Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.00000014, -0.00000014}
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