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Simplifying 2x2 + 37x = 35 Reorder the terms: 37x + 2x2 = 35 Solving 37x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 37x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 37x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 18.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 18.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 18.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 18.5x + x2 = 0 + 17.5 18.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 18.5x + x2 = 17.5 The x term is 18.5x. Take half its coefficient (9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. 18.5x + 85.5625 + x2 = 17.5 + 85.5625 Reorder the terms: 85.5625 + 18.5x + x2 = 17.5 + 85.5625 Combine like terms: 17.5 + 85.5625 = 103.0625 85.5625 + 18.5x + x2 = 103.0625 Factor a perfect square on the left side: (x + 9.25)(x + 9.25) = 103.0625 Calculate the square root of the right side: 10.151970252 Break this problem into two subproblems by setting (x + 9.25) equal to 10.151970252 and -10.151970252.Subproblem 1
x + 9.25 = 10.151970252 Simplifying x + 9.25 = 10.151970252 Reorder the terms: 9.25 + x = 10.151970252 Solving 9.25 + x = 10.151970252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = 10.151970252 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = 10.151970252 + -9.25 x = 10.151970252 + -9.25 Combine like terms: 10.151970252 + -9.25 = 0.901970252 x = 0.901970252 Simplifying x = 0.901970252Subproblem 2
x + 9.25 = -10.151970252 Simplifying x + 9.25 = -10.151970252 Reorder the terms: 9.25 + x = -10.151970252 Solving 9.25 + x = -10.151970252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.25' to each side of the equation. 9.25 + -9.25 + x = -10.151970252 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + x = -10.151970252 + -9.25 x = -10.151970252 + -9.25 Combine like terms: -10.151970252 + -9.25 = -19.401970252 x = -19.401970252 Simplifying x = -19.401970252Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.901970252, -19.401970252}
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