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Simplifying x2 + 7x + -13 = 2x Reorder the terms: -13 + 7x + x2 = 2x Solving -13 + 7x + x2 = 2x Solving for variable 'x'. Reorder the terms: -13 + 7x + -2x + x2 = 2x + -2x Combine like terms: 7x + -2x = 5x -13 + 5x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -13 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 5x + x2 = 0 + 13 5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 5x + x2 = 13 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 13 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 13 + 6.25 Combine like terms: 13 + 6.25 = 19.25 6.25 + 5x + x2 = 19.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + 2.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + 2.5 = 4.387482194 Simplifying x + 2.5 = 4.387482194 Reorder the terms: 2.5 + x = 4.387482194 Solving 2.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.387482194 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.387482194 + -2.5 x = 4.387482194 + -2.5 Combine like terms: 4.387482194 + -2.5 = 1.887482194 x = 1.887482194 Simplifying x = 1.887482194Subproblem 2
x + 2.5 = -4.387482194 Simplifying x + 2.5 = -4.387482194 Reorder the terms: 2.5 + x = -4.387482194 Solving 2.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.387482194 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.387482194 + -2.5 x = -4.387482194 + -2.5 Combine like terms: -4.387482194 + -2.5 = -6.887482194 x = -6.887482194 Simplifying x = -6.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.887482194, -6.887482194}
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