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Simplifying 2x(x + 10) = 75 Reorder the terms: 2x(10 + x) = 75 (10 * 2x + x * 2x) = 75 (20x + 2x2) = 75 Solving 20x + 2x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 20x + 2x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + 10x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 10x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 10x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 10x + x2 = 0 + 37.5 10x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 10x + x2 = 37.5 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 = 37.5 + 25 Reorder the terms: 25 + 10x + x2 = 37.5 + 25 Combine like terms: 37.5 + 25 = 62.5 25 + 10x + x2 = 62.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + 5) equal to 7.90569415 and -7.90569415.Subproblem 1
x + 5 = 7.90569415 Simplifying x + 5 = 7.90569415 Reorder the terms: 5 + x = 7.90569415 Solving 5 + x = 7.90569415 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 = 7.90569415 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.90569415 + -5 x = 7.90569415 + -5 Combine like terms: 7.90569415 + -5 = 2.90569415 x = 2.90569415 Simplifying x = 2.90569415Subproblem 2
x + 5 = -7.90569415 Simplifying x + 5 = -7.90569415 Reorder the terms: 5 + x = -7.90569415 Solving 5 + x = -7.90569415 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 = -7.90569415 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.90569415 + -5 x = -7.90569415 + -5 Combine like terms: -7.90569415 + -5 = -12.90569415 x = -12.90569415 Simplifying x = -12.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.90569415, -12.90569415}
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