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Simplifying 2x2 + -1x = 34 Reorder the terms: -1x + 2x2 = 34 Solving -1x + 2x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + -1x + 2x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17 + -0.5x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -0.5x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -0.5x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -0.5x + x2 = 0 + 17 -0.5x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -0.5x + x2 = 17 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 17 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 17 + 0.0625 Combine like terms: 17 + 0.0625 = 17.0625 0.0625 + -0.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + -0.25) equal to 4.13067791 and -4.13067791.Subproblem 1
x + -0.25 = 4.13067791 Simplifying x + -0.25 = 4.13067791 Reorder the terms: -0.25 + x = 4.13067791 Solving -0.25 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.13067791 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.13067791 + 0.25 x = 4.13067791 + 0.25 Combine like terms: 4.13067791 + 0.25 = 4.38067791 x = 4.38067791 Simplifying x = 4.38067791Subproblem 2
x + -0.25 = -4.13067791 Simplifying x + -0.25 = -4.13067791 Reorder the terms: -0.25 + x = -4.13067791 Solving -0.25 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.13067791 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.13067791 + 0.25 x = -4.13067791 + 0.25 Combine like terms: -4.13067791 + 0.25 = -3.88067791 x = -3.88067791 Simplifying x = -3.88067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.38067791, -3.88067791}
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