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Simplifying 2x2 + 13x + -18 = 0 Reorder the terms: -18 + 13x + 2x2 = 0 Solving -18 + 13x + 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'. -9 + 6.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 6.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 6.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6.5x + x2 = 0 + 9 6.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 6.5x + x2 = 9 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 9 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 9 + 10.5625 Combine like terms: 9 + 10.5625 = 19.5625 10.5625 + 6.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + 3.25) equal to 4.422951503 and -4.422951503.Subproblem 1
x + 3.25 = 4.422951503 Simplifying x + 3.25 = 4.422951503 Reorder the terms: 3.25 + x = 4.422951503 Solving 3.25 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 4.422951503 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.422951503 + -3.25 x = 4.422951503 + -3.25 Combine like terms: 4.422951503 + -3.25 = 1.172951503 x = 1.172951503 Simplifying x = 1.172951503Subproblem 2
x + 3.25 = -4.422951503 Simplifying x + 3.25 = -4.422951503 Reorder the terms: 3.25 + x = -4.422951503 Solving 3.25 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -4.422951503 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.422951503 + -3.25 x = -4.422951503 + -3.25 Combine like terms: -4.422951503 + -3.25 = -7.672951503 x = -7.672951503 Simplifying x = -7.672951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.172951503, -7.672951503}
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