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Simplifying (2x2) + -7x = 2 Reorder the terms: -7x + (2x2) = 2 Solving -7x + (2x2) = 2 Solving for variable 'x'. Reorder the terms: -2 + -7x + (2x2) = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -7x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -3.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.5x + x2 = 0 + 1 -3.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.5x + x2 = 1 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 = 1 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 1 + 3.0625 Combine like terms: 1 + 3.0625 = 4.0625 3.0625 + -3.5x + x2 = 4.0625 Factor a perfect square on the left side: ((x) + -1.75)((x) + -1.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting ((x) + -1.75) equal to 2.015564437 and -2.015564437.Subproblem 1
(x) + -1.75 = 2.015564437 Simplifying (x) + -1.75 = 2.015564437 x + -1.75 = 2.015564437 Reorder the terms: -1.75 + x = 2.015564437 Solving -1.75 + x = 2.015564437 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 = 2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.015564437 + 1.75 x = 2.015564437 + 1.75 Combine like terms: 2.015564437 + 1.75 = 3.765564437 x = 3.765564437 Simplifying x = 3.765564437Subproblem 2
(x) + -1.75 = -2.015564437 Simplifying (x) + -1.75 = -2.015564437 x + -1.75 = -2.015564437 Reorder the terms: -1.75 + x = -2.015564437 Solving -1.75 + x = -2.015564437 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 = -2.015564437 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.015564437 + 1.75 x = -2.015564437 + 1.75 Combine like terms: -2.015564437 + 1.75 = -0.265564437 x = -0.265564437 Simplifying x = -0.265564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.765564437, -0.265564437}
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