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Simplifying x(2x + 5) = 340 Reorder the terms: x(5 + 2x) = 340 (5 * x + 2x * x) = 340 (5x + 2x2) = 340 Solving 5x + 2x2 = 340 Solving for variable 'x'. Reorder the terms: -340 + 5x + 2x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -340 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -170 + 2.5x + x2 = 0 Move the constant term to the right: Add '170' to each side of the equation. -170 + 2.5x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 2.5x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 2.5x + x2 = 0 + 170 2.5x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 2.5x + x2 = 170 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 = 170 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 170 + 1.5625 Combine like terms: 170 + 1.5625 = 171.5625 1.5625 + 2.5x + x2 = 171.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 171.5625 Calculate the square root of the right side: 13.098186897 Break this problem into two subproblems by setting (x + 1.25) equal to 13.098186897 and -13.098186897.Subproblem 1
x + 1.25 = 13.098186897 Simplifying x + 1.25 = 13.098186897 Reorder the terms: 1.25 + x = 13.098186897 Solving 1.25 + x = 13.098186897 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 = 13.098186897 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 13.098186897 + -1.25 x = 13.098186897 + -1.25 Combine like terms: 13.098186897 + -1.25 = 11.848186897 x = 11.848186897 Simplifying x = 11.848186897Subproblem 2
x + 1.25 = -13.098186897 Simplifying x + 1.25 = -13.098186897 Reorder the terms: 1.25 + x = -13.098186897 Solving 1.25 + x = -13.098186897 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 = -13.098186897 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -13.098186897 + -1.25 x = -13.098186897 + -1.25 Combine like terms: -13.098186897 + -1.25 = -14.348186897 x = -14.348186897 Simplifying x = -14.348186897Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.848186897, -14.348186897}
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