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Simplifying x(2x + 5) = 34 Reorder the terms: x(5 + 2x) = 34 (5 * x + 2x * x) = 34 (5x + 2x2) = 34 Solving 5x + 2x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 5x + 2x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17 + 2.5x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 2.5x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 2.5x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2.5x + x2 = 0 + 17 2.5x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 2.5x + x2 = 17 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 17 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 17 + 1.5625 Combine like terms: 17 + 1.5625 = 18.5625 1.5625 + 2.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + 1.25) equal to 4.308421985 and -4.308421985.Subproblem 1
x + 1.25 = 4.308421985 Simplifying x + 1.25 = 4.308421985 Reorder the terms: 1.25 + x = 4.308421985 Solving 1.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.308421985 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.308421985 + -1.25 x = 4.308421985 + -1.25 Combine like terms: 4.308421985 + -1.25 = 3.058421985 x = 3.058421985 Simplifying x = 3.058421985Subproblem 2
x + 1.25 = -4.308421985 Simplifying x + 1.25 = -4.308421985 Reorder the terms: 1.25 + x = -4.308421985 Solving 1.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.308421985 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.308421985 + -1.25 x = -4.308421985 + -1.25 Combine like terms: -4.308421985 + -1.25 = -5.558421985 x = -5.558421985 Simplifying x = -5.558421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.058421985, -5.558421985}
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