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Simplifying (2x * x) + -4x = 7 Multiply x * x (2x2) + -4x = 7 Reorder the terms: -4x + (2x2) = 7 Solving -4x + (2x2) = 7 Solving for variable 'x'. Reorder the terms: -7 + -4x + (2x2) = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -4x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -2x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2x + x2 = 0 + 3.5 -2x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2x + x2 = 3.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.5 + 1 Reorder the terms: 1 + -2x + x2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + -2x + x2 = 4.5 Factor a perfect square on the left side: ((x) + -1)((x) + -1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting ((x) + -1) equal to 2.121320344 and -2.121320344.Subproblem 1
(x) + -1 = 2.121320344 Simplifying (x) + -1 = 2.121320344 x + -1 = 2.121320344 Reorder the terms: -1 + x = 2.121320344 Solving -1 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.121320344 + 1 x = 2.121320344 + 1 Combine like terms: 2.121320344 + 1 = 3.121320344 x = 3.121320344 Simplifying x = 3.121320344Subproblem 2
(x) + -1 = -2.121320344 Simplifying (x) + -1 = -2.121320344 x + -1 = -2.121320344 Reorder the terms: -1 + x = -2.121320344 Solving -1 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.121320344 + 1 x = -2.121320344 + 1 Combine like terms: -2.121320344 + 1 = -1.121320344 x = -1.121320344 Simplifying x = -1.121320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.121320344, -1.121320344}
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