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Simplifying 10x2 + -50x = 1 Reorder the terms: -50x + 10x2 = 1 Solving -50x + 10x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -50x + 10x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -50x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -5x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -5x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -5x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -5x + x2 = 0 + 0.1 -5x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -5x + x2 = 0.1 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.1 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.1 + 6.25 Combine like terms: 0.1 + 6.25 = 6.35 6.25 + -5x + x2 = 6.35 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.35 Calculate the square root of the right side: 2.519920634 Break this problem into two subproblems by setting (x + -2.5) equal to 2.519920634 and -2.519920634.Subproblem 1
x + -2.5 = 2.519920634 Simplifying x + -2.5 = 2.519920634 Reorder the terms: -2.5 + x = 2.519920634 Solving -2.5 + x = 2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.519920634 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.519920634 + 2.5 x = 2.519920634 + 2.5 Combine like terms: 2.519920634 + 2.5 = 5.019920634 x = 5.019920634 Simplifying x = 5.019920634Subproblem 2
x + -2.5 = -2.519920634 Simplifying x + -2.5 = -2.519920634 Reorder the terms: -2.5 + x = -2.519920634 Solving -2.5 + x = -2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.519920634 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.519920634 + 2.5 x = -2.519920634 + 2.5 Combine like terms: -2.519920634 + 2.5 = -0.019920634 x = -0.019920634 Simplifying x = -0.019920634Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.019920634, -0.019920634}
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