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Simplifying (10x + -1) * x = 30 Reorder the terms: (-1 + 10x) * x = 30 Reorder the terms for easier multiplication: x(-1 + 10x) = 30 (-1 * x + 10x * x) = 30 (-1x + 10x2) = 30 Solving -1x + 10x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -1x + 10x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -1x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3 + -0.1x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.1x + x2 = 0 + 3 -0.1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.1x + x2 = 3 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 3 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 3 + 0.0025 Combine like terms: 3 + 0.0025 = 3.0025 0.0025 + -0.1x + x2 = 3.0025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 3.0025 Calculate the square root of the right side: 1.732772345 Break this problem into two subproblems by setting (x + -0.05) equal to 1.732772345 and -1.732772345.Subproblem 1
x + -0.05 = 1.732772345 Simplifying x + -0.05 = 1.732772345 Reorder the terms: -0.05 + x = 1.732772345 Solving -0.05 + x = 1.732772345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 1.732772345 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 1.732772345 + 0.05 x = 1.732772345 + 0.05 Combine like terms: 1.732772345 + 0.05 = 1.782772345 x = 1.782772345 Simplifying x = 1.782772345Subproblem 2
x + -0.05 = -1.732772345 Simplifying x + -0.05 = -1.732772345 Reorder the terms: -0.05 + x = -1.732772345 Solving -0.05 + x = -1.732772345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -1.732772345 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -1.732772345 + 0.05 x = -1.732772345 + 0.05 Combine like terms: -1.732772345 + 0.05 = -1.682772345 x = -1.682772345 Simplifying x = -1.682772345Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.782772345, -1.682772345}
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