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Simplifying 2x2 + 2x + 1 = 340 Reorder the terms: 1 + 2x + 2x2 = 340 Solving 1 + 2x + 2x2 = 340 Solving for variable 'x'. Reorder the terms: 1 + -340 + 2x + 2x2 = 340 + -340 Combine like terms: 1 + -340 = -339 -339 + 2x + 2x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -339 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -169.5 + x + x2 = 0 Move the constant term to the right: Add '169.5' to each side of the equation. -169.5 + x + 169.5 + x2 = 0 + 169.5 Reorder the terms: -169.5 + 169.5 + x + x2 = 0 + 169.5 Combine like terms: -169.5 + 169.5 = 0.0 0.0 + x + x2 = 0 + 169.5 x + x2 = 0 + 169.5 Combine like terms: 0 + 169.5 = 169.5 x + x2 = 169.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 169.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 169.5 + 0.25 Combine like terms: 169.5 + 0.25 = 169.75 1.25 + x2 = 169.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 169.75 Calculate the square root of the right side: 13.028814221 Break this problem into two subproblems by setting (x + 0.5) equal to 13.028814221 and -13.028814221.Subproblem 1
x + 0.5 = 13.028814221 Simplifying x + 0.5 = 13.028814221 Reorder the terms: 0.5 + x = 13.028814221 Solving 0.5 + x = 13.028814221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.028814221 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.028814221 + -0.5 x = 13.028814221 + -0.5 Combine like terms: 13.028814221 + -0.5 = 12.528814221 x = 12.528814221 Simplifying x = 12.528814221Subproblem 2
x + 0.5 = -13.028814221 Simplifying x + 0.5 = -13.028814221 Reorder the terms: 0.5 + x = -13.028814221 Solving 0.5 + x = -13.028814221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.028814221 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.028814221 + -0.5 x = -13.028814221 + -0.5 Combine like terms: -13.028814221 + -0.5 = -13.528814221 x = -13.528814221 Simplifying x = -13.528814221Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.528814221, -13.528814221}
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