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Simplifying 2x2 + -7x = 33 Reorder the terms: -7x + 2x2 = 33 Solving -7x + 2x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -7x + 2x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -3.5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -3.5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -3.5x + x2 = 0 + 16.5 -3.5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -3.5x + x2 = 16.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 16.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 16.5 + 3.0625 Combine like terms: 16.5 + 3.0625 = 19.5625 3.0625 + -3.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + -1.75) equal to 4.422951503 and -4.422951503.Subproblem 1
x + -1.75 = 4.422951503 Simplifying x + -1.75 = 4.422951503 Reorder the terms: -1.75 + x = 4.422951503 Solving -1.75 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.422951503 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.422951503 + 1.75 x = 4.422951503 + 1.75 Combine like terms: 4.422951503 + 1.75 = 6.172951503 x = 6.172951503 Simplifying x = 6.172951503Subproblem 2
x + -1.75 = -4.422951503 Simplifying x + -1.75 = -4.422951503 Reorder the terms: -1.75 + x = -4.422951503 Solving -1.75 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.422951503 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.422951503 + 1.75 x = -4.422951503 + 1.75 Combine like terms: -4.422951503 + 1.75 = -2.672951503 x = -2.672951503 Simplifying x = -2.672951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.172951503, -2.672951503}
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