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Simplifying 2x2 + -5x + -36 = 0 Reorder the terms: -36 + -5x + 2x2 = 0 Solving -36 + -5x + 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 + -2.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -2.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -2.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2.5x + x2 = 0 + 18 -2.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2.5x + x2 = 18 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 18 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 18 + 1.5625 Combine like terms: 18 + 1.5625 = 19.5625 1.5625 + -2.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + -1.25) equal to 4.422951503 and -4.422951503.Subproblem 1
x + -1.25 = 4.422951503 Simplifying x + -1.25 = 4.422951503 Reorder the terms: -1.25 + x = 4.422951503 Solving -1.25 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.422951503 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.422951503 + 1.25 x = 4.422951503 + 1.25 Combine like terms: 4.422951503 + 1.25 = 5.672951503 x = 5.672951503 Simplifying x = 5.672951503Subproblem 2
x + -1.25 = -4.422951503 Simplifying x + -1.25 = -4.422951503 Reorder the terms: -1.25 + x = -4.422951503 Solving -1.25 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.422951503 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.422951503 + 1.25 x = -4.422951503 + 1.25 Combine like terms: -4.422951503 + 1.25 = -3.172951503 x = -3.172951503 Simplifying x = -3.172951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.672951503, -3.172951503}
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