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Simplifying 2x2 + 17x + -74 = 0 Reorder the terms: -74 + 17x + 2x2 = 0 Solving -74 + 17x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37 + 8.5x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + 8.5x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 8.5x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 8.5x + x2 = 0 + 37 8.5x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 8.5x + x2 = 37 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 = 37 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 37 + 18.0625 Combine like terms: 37 + 18.0625 = 55.0625 18.0625 + 8.5x + x2 = 55.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 55.0625 Calculate the square root of the right side: 7.42041104 Break this problem into two subproblems by setting (x + 4.25) equal to 7.42041104 and -7.42041104.Subproblem 1
x + 4.25 = 7.42041104 Simplifying x + 4.25 = 7.42041104 Reorder the terms: 4.25 + x = 7.42041104 Solving 4.25 + x = 7.42041104 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 = 7.42041104 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 7.42041104 + -4.25 x = 7.42041104 + -4.25 Combine like terms: 7.42041104 + -4.25 = 3.17041104 x = 3.17041104 Simplifying x = 3.17041104Subproblem 2
x + 4.25 = -7.42041104 Simplifying x + 4.25 = -7.42041104 Reorder the terms: 4.25 + x = -7.42041104 Solving 4.25 + x = -7.42041104 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 = -7.42041104 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -7.42041104 + -4.25 x = -7.42041104 + -4.25 Combine like terms: -7.42041104 + -4.25 = -11.67041104 x = -11.67041104 Simplifying x = -11.67041104Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17041104, -11.67041104}
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