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Simplifying (x + -1)(x + -1) = 5x + -7 Reorder the terms: (-1 + x)(x + -1) = 5x + -7 Reorder the terms: (-1 + x)(-1 + x) = 5x + -7 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) = 5x + -7 ((-1 * -1 + x * -1) + x(-1 + x)) = 5x + -7 ((1 + -1x) + x(-1 + x)) = 5x + -7 (1 + -1x + (-1 * x + x * x)) = 5x + -7 (1 + -1x + (-1x + x2)) = 5x + -7 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) = 5x + -7 Reorder the terms: 1 + -2x + x2 = -7 + 5x Solving 1 + -2x + x2 = -7 + 5x Solving for variable 'x'. Reorder the terms: 1 + 7 + -2x + -5x + x2 = -7 + 5x + 7 + -5x Combine like terms: 1 + 7 = 8 8 + -2x + -5x + x2 = -7 + 5x + 7 + -5x Combine like terms: -2x + -5x = -7x 8 + -7x + x2 = -7 + 5x + 7 + -5x Reorder the terms: 8 + -7x + x2 = -7 + 7 + 5x + -5x Combine like terms: -7 + 7 = 0 8 + -7x + x2 = 0 + 5x + -5x 8 + -7x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 8 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -7x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7x + x2 = 0 + -8 -7x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7x + x2 = -8 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -8 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7x + x2 = 4.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -3.5 = 2.061552813 Simplifying x + -3.5 = 2.061552813 Reorder the terms: -3.5 + x = 2.061552813 Solving -3.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.061552813 + 3.5 x = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 x = 5.561552813 Simplifying x = 5.561552813Subproblem 2
x + -3.5 = -2.061552813 Simplifying x + -3.5 = -2.061552813 Reorder the terms: -3.5 + x = -2.061552813 Solving -3.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.061552813 + 3.5 x = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 x = 1.438447187 Simplifying x = 1.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.561552813, 1.438447187}
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