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Simplifying (x + -1)(x + -1) = 7x Reorder the terms: (-1 + x)(x + -1) = 7x Reorder the terms: (-1 + x)(-1 + x) = 7x Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) = 7x ((-1 * -1 + x * -1) + x(-1 + x)) = 7x ((1 + -1x) + x(-1 + x)) = 7x (1 + -1x + (-1 * x + x * x)) = 7x (1 + -1x + (-1x + x2)) = 7x Combine like terms: -1x + -1x = -2x (1 + -2x + x2) = 7x Solving 1 + -2x + x2 = 7x Solving for variable 'x'. Reorder the terms: 1 + -2x + -7x + x2 = 7x + -7x Combine like terms: -2x + -7x = -9x 1 + -9x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 1 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -9x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -9x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x + x2 = 0 + -1 -9x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9x + x2 = -1 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -1 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + -9x + x2 = 19.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -4.5 = 4.387482194 Simplifying x + -4.5 = 4.387482194 Reorder the terms: -4.5 + x = 4.387482194 Solving -4.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.387482194 + 4.5 x = 4.387482194 + 4.5 Combine like terms: 4.387482194 + 4.5 = 8.887482194 x = 8.887482194 Simplifying x = 8.887482194Subproblem 2
x + -4.5 = -4.387482194 Simplifying x + -4.5 = -4.387482194 Reorder the terms: -4.5 + x = -4.387482194 Solving -4.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.387482194 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.387482194 + 4.5 x = -4.387482194 + 4.5 Combine like terms: -4.387482194 + 4.5 = 0.112517806 x = 0.112517806 Simplifying x = 0.112517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.887482194, 0.112517806}
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