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Simplifying 2x2 + 17x + -36 = 0 Reorder the terms: -36 + 17x + 2x2 = 0 Solving -36 + 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'. -18 + 8.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 8.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 8.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 8.5x + x2 = 0 + 18 8.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 8.5x + x2 = 18 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 = 18 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 18 + 18.0625 Combine like terms: 18 + 18.0625 = 36.0625 18.0625 + 8.5x + x2 = 36.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 36.0625 Calculate the square root of the right side: 6.005206075 Break this problem into two subproblems by setting (x + 4.25) equal to 6.005206075 and -6.005206075.Subproblem 1
x + 4.25 = 6.005206075 Simplifying x + 4.25 = 6.005206075 Reorder the terms: 4.25 + x = 6.005206075 Solving 4.25 + x = 6.005206075 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 = 6.005206075 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 6.005206075 + -4.25 x = 6.005206075 + -4.25 Combine like terms: 6.005206075 + -4.25 = 1.755206075 x = 1.755206075 Simplifying x = 1.755206075Subproblem 2
x + 4.25 = -6.005206075 Simplifying x + 4.25 = -6.005206075 Reorder the terms: 4.25 + x = -6.005206075 Solving 4.25 + x = -6.005206075 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 = -6.005206075 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -6.005206075 + -4.25 x = -6.005206075 + -4.25 Combine like terms: -6.005206075 + -4.25 = -10.255206075 x = -10.255206075 Simplifying x = -10.255206075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.755206075, -10.255206075}
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