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Simplifying x(2x + 10) = 25 Reorder the terms: x(10 + 2x) = 25 (10 * x + 2x * x) = 25 (10x + 2x2) = 25 Solving 10x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 10x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 5x + x2 = 0 + 12.5 5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 5x + x2 = 12.5 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 = 12.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 12.5 + 6.25 Combine like terms: 12.5 + 6.25 = 18.75 6.25 + 5x + x2 = 18.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + 2.5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + 2.5 = 4.330127019 Simplifying x + 2.5 = 4.330127019 Reorder the terms: 2.5 + x = 4.330127019 Solving 2.5 + x = 4.330127019 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 = 4.330127019 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.330127019 + -2.5 x = 4.330127019 + -2.5 Combine like terms: 4.330127019 + -2.5 = 1.830127019 x = 1.830127019 Simplifying x = 1.830127019Subproblem 2
x + 2.5 = -4.330127019 Simplifying x + 2.5 = -4.330127019 Reorder the terms: 2.5 + x = -4.330127019 Solving 2.5 + x = -4.330127019 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 = -4.330127019 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.330127019 + -2.5 x = -4.330127019 + -2.5 Combine like terms: -4.330127019 + -2.5 = -6.830127019 x = -6.830127019 Simplifying x = -6.830127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.830127019, -6.830127019}
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