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Simplifying -6x + -7 = x + -1x2 Reorder the terms: -7 + -6x = x + -1x2 Solving -7 + -6x = x + -1x2 Solving for variable 'x'. Combine like terms: -6x + -1x = -7x -7 + -7x + x2 = x + -1x2 + -1x + x2 Reorder the terms: -7 + -7x + x2 = x + -1x + -1x2 + x2 Combine like terms: x + -1x = 0 -7 + -7x + x2 = 0 + -1x2 + x2 -7 + -7x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -7 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -7x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -7x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -7x + x2 = 0 + 7 -7x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -7x + x2 = 7 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 = 7 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 7 + 12.25 Combine like terms: 7 + 12.25 = 19.25 12.25 + -7x + x2 = 19.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -3.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -3.5 = 4.387482194 Simplifying x + -3.5 = 4.387482194 Reorder the terms: -3.5 + x = 4.387482194 Solving -3.5 + x = 4.387482194 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 = 4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.387482194 + 3.5 x = 4.387482194 + 3.5 Combine like terms: 4.387482194 + 3.5 = 7.887482194 x = 7.887482194 Simplifying x = 7.887482194Subproblem 2
x + -3.5 = -4.387482194 Simplifying x + -3.5 = -4.387482194 Reorder the terms: -3.5 + x = -4.387482194 Solving -3.5 + x = -4.387482194 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 = -4.387482194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.387482194 + 3.5 x = -4.387482194 + 3.5 Combine like terms: -4.387482194 + 3.5 = -0.887482194 x = -0.887482194 Simplifying x = -0.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.887482194, -0.887482194}
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