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Simplifying 0 = 4x2 + 34x + -11 Reorder the terms: 0 = -11 + 34x + 4x2 Solving 0 = -11 + 34x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + -34x + -4x2 = -11 + 34x + 4x2 + 11 + -34x + -4x2 Reorder the terms: 11 + -34x + -4x2 = -11 + 11 + 34x + -34x + 4x2 + -4x2 Combine like terms: -11 + 11 = 0 11 + -34x + -4x2 = 0 + 34x + -34x + 4x2 + -4x2 11 + -34x + -4x2 = 34x + -34x + 4x2 + -4x2 Combine like terms: 34x + -34x = 0 11 + -34x + -4x2 = 0 + 4x2 + -4x2 11 + -34x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 11 + -34x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + 8.5x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 8.5x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 8.5x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 8.5x + x2 = 0 + 2.75 8.5x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 8.5x + x2 = 2.75 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 2.75 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 2.75 + 18.0625 Combine like terms: 2.75 + 18.0625 = 20.8125 18.0625 + 8.5x + x2 = 20.8125 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 20.8125 Calculate the square root of the right side: 4.562071898 Break this problem into two subproblems by setting (x + 4.25) equal to 4.562071898 and -4.562071898.Subproblem 1
x + 4.25 = 4.562071898 Simplifying x + 4.25 = 4.562071898 Reorder the terms: 4.25 + x = 4.562071898 Solving 4.25 + x = 4.562071898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.562071898 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.562071898 + -4.25 x = 4.562071898 + -4.25 Combine like terms: 4.562071898 + -4.25 = 0.312071898 x = 0.312071898 Simplifying x = 0.312071898Subproblem 2
x + 4.25 = -4.562071898 Simplifying x + 4.25 = -4.562071898 Reorder the terms: 4.25 + x = -4.562071898 Solving 4.25 + x = -4.562071898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.562071898 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.562071898 + -4.25 x = -4.562071898 + -4.25 Combine like terms: -4.562071898 + -4.25 = -8.812071898 x = -8.812071898 Simplifying x = -8.812071898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.312071898, -8.812071898}
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