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Simplifying x2 + 15x + 17 = 7x + 3 Reorder the terms: 17 + 15x + x2 = 7x + 3 Reorder the terms: 17 + 15x + x2 = 3 + 7x Solving 17 + 15x + x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: 17 + -3 + 15x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: 17 + -3 = 14 14 + 15x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: 15x + -7x = 8x 14 + 8x + x2 = 3 + 7x + -3 + -7x Reorder the terms: 14 + 8x + x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 14 + 8x + x2 = 0 + 7x + -7x 14 + 8x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 14 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 8x + x2 = 0 + -14 8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 8x + x2 = -14 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -14 + 16 Reorder the terms: 16 + 8x + x2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + 8x + x2 = 2 Factor a perfect square on the left side: (x + 4)(x + 4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 4 = 1.414213562 Simplifying x + 4 = 1.414213562 Reorder the terms: 4 + x = 1.414213562 Solving 4 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.414213562 + -4 x = 1.414213562 + -4 Combine like terms: 1.414213562 + -4 = -2.585786438 x = -2.585786438 Simplifying x = -2.585786438Subproblem 2
x + 4 = -1.414213562 Simplifying x + 4 = -1.414213562 Reorder the terms: 4 + x = -1.414213562 Solving 4 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.414213562 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.414213562 + -4 x = -1.414213562 + -4 Combine like terms: -1.414213562 + -4 = -5.414213562 x = -5.414213562 Simplifying x = -5.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.585786438, -5.414213562}
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