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Simplifying x2 + 3x + -1 = 7x + 22 Reorder the terms: -1 + 3x + x2 = 7x + 22 Reorder the terms: -1 + 3x + x2 = 22 + 7x Solving -1 + 3x + x2 = 22 + 7x Solving for variable 'x'. Reorder the terms: -1 + -22 + 3x + -7x + x2 = 22 + 7x + -22 + -7x Combine like terms: -1 + -22 = -23 -23 + 3x + -7x + x2 = 22 + 7x + -22 + -7x Combine like terms: 3x + -7x = -4x -23 + -4x + x2 = 22 + 7x + -22 + -7x Reorder the terms: -23 + -4x + x2 = 22 + -22 + 7x + -7x Combine like terms: 22 + -22 = 0 -23 + -4x + x2 = 0 + 7x + -7x -23 + -4x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -23 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -4x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -4x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -4x + x2 = 0 + 23 -4x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -4x + x2 = 23 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 23 + 4 Reorder the terms: 4 + -4x + x2 = 23 + 4 Combine like terms: 23 + 4 = 27 4 + -4x + x2 = 27 Factor a perfect square on the left side: (x + -2)(x + -2) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -2) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -2 = 5.196152423 Simplifying x + -2 = 5.196152423 Reorder the terms: -2 + x = 5.196152423 Solving -2 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.196152423 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.196152423 + 2 x = 5.196152423 + 2 Combine like terms: 5.196152423 + 2 = 7.196152423 x = 7.196152423 Simplifying x = 7.196152423Subproblem 2
x + -2 = -5.196152423 Simplifying x + -2 = -5.196152423 Reorder the terms: -2 + x = -5.196152423 Solving -2 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.196152423 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.196152423 + 2 x = -5.196152423 + 2 Combine like terms: -5.196152423 + 2 = -3.196152423 x = -3.196152423 Simplifying x = -3.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.196152423, -3.196152423}
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