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Simplifying (10x + -1) * 5x = 9 Reorder the terms: (-1 + 10x) * 5x = 9 Reorder the terms for easier multiplication: 5x(-1 + 10x) = 9 (-1 * 5x + 10x * 5x) = 9 (-5x + 50x2) = 9 Solving -5x + 50x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -5x + 50x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -5x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.18 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '0.18' to each side of the equation. -0.18 + -0.1x + 0.18 + x2 = 0.0 + 0.18 Reorder the terms: -0.18 + 0.18 + -0.1x + x2 = 0.0 + 0.18 Combine like terms: -0.18 + 0.18 = 0.00 0.00 + -0.1x + x2 = 0.0 + 0.18 -0.1x + x2 = 0.0 + 0.18 Combine like terms: 0.0 + 0.18 = 0.18 -0.1x + x2 = 0.18 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 = 0.18 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.18 + 0.0025 Combine like terms: 0.18 + 0.0025 = 0.1825 0.0025 + -0.1x + x2 = 0.1825 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.1825 Calculate the square root of the right side: 0.427200187 Break this problem into two subproblems by setting (x + -0.05) equal to 0.427200187 and -0.427200187.Subproblem 1
x + -0.05 = 0.427200187 Simplifying x + -0.05 = 0.427200187 Reorder the terms: -0.05 + x = 0.427200187 Solving -0.05 + x = 0.427200187 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 = 0.427200187 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.427200187 + 0.05 x = 0.427200187 + 0.05 Combine like terms: 0.427200187 + 0.05 = 0.477200187 x = 0.477200187 Simplifying x = 0.477200187Subproblem 2
x + -0.05 = -0.427200187 Simplifying x + -0.05 = -0.427200187 Reorder the terms: -0.05 + x = -0.427200187 Solving -0.05 + x = -0.427200187 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 = -0.427200187 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.427200187 + 0.05 x = -0.427200187 + 0.05 Combine like terms: -0.427200187 + 0.05 = -0.377200187 x = -0.377200187 Simplifying x = -0.377200187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.477200187, -0.377200187}
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