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Simplifying x2 + -1x = 7 + x Reorder the terms: -1x + x2 = 7 + x Solving -1x + x2 = 7 + x Solving for variable 'x'. Reorder the terms: -7 + -1x + -1x + x2 = 7 + x + -7 + -1x Combine like terms: -1x + -1x = -2x -7 + -2x + x2 = 7 + x + -7 + -1x Reorder the terms: -7 + -2x + x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -7 + -2x + x2 = 0 + x + -1x -7 + -2x + x2 = x + -1x Combine like terms: x + -1x = 0 -7 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x + x2 = 0 + 7 -2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2x + x2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2x + x2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2x + x2 = 8 Factor a perfect square on the left side: (x + -1)(x + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -1 = 2.828427125 Simplifying x + -1 = 2.828427125 Reorder the terms: -1 + x = 2.828427125 Solving -1 + x = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.828427125 + 1 x = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 x = 3.828427125 Simplifying x = 3.828427125Subproblem 2
x + -1 = -2.828427125 Simplifying x + -1 = -2.828427125 Reorder the terms: -1 + x = -2.828427125 Solving -1 + x = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.828427125 + 1 x = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 x = -1.828427125 Simplifying x = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.828427125, -1.828427125}
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