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Simplifying (x + -15)(x + -15) = 2 Reorder the terms: (-15 + x)(x + -15) = 2 Reorder the terms: (-15 + x)(-15 + x) = 2 Multiply (-15 + x) * (-15 + x) (-15(-15 + x) + x(-15 + x)) = 2 ((-15 * -15 + x * -15) + x(-15 + x)) = 2 ((225 + -15x) + x(-15 + x)) = 2 (225 + -15x + (-15 * x + x * x)) = 2 (225 + -15x + (-15x + x2)) = 2 Combine like terms: -15x + -15x = -30x (225 + -30x + x2) = 2 Solving 225 + -30x + x2 = 2 Solving for variable 'x'. Reorder the terms: 225 + -2 + -30x + x2 = 2 + -2 Combine like terms: 225 + -2 = 223 223 + -30x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 223 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-223' to each side of the equation. 223 + -30x + -223 + x2 = 0 + -223 Reorder the terms: 223 + -223 + -30x + x2 = 0 + -223 Combine like terms: 223 + -223 = 0 0 + -30x + x2 = 0 + -223 -30x + x2 = 0 + -223 Combine like terms: 0 + -223 = -223 -30x + x2 = -223 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -223 + 225 Reorder the terms: 225 + -30x + x2 = -223 + 225 Combine like terms: -223 + 225 = 2 225 + -30x + x2 = 2 Factor a perfect square on the left side: (x + -15)(x + -15) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -15) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -15 = 1.414213562 Simplifying x + -15 = 1.414213562 Reorder the terms: -15 + x = 1.414213562 Solving -15 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 1.414213562 + 15 Combine like terms: -15 + 15 = 0 0 + x = 1.414213562 + 15 x = 1.414213562 + 15 Combine like terms: 1.414213562 + 15 = 16.414213562 x = 16.414213562 Simplifying x = 16.414213562Subproblem 2
x + -15 = -1.414213562 Simplifying x + -15 = -1.414213562 Reorder the terms: -15 + x = -1.414213562 Solving -15 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -1.414213562 + 15 Combine like terms: -15 + 15 = 0 0 + x = -1.414213562 + 15 x = -1.414213562 + 15 Combine like terms: -1.414213562 + 15 = 13.585786438 x = 13.585786438 Simplifying x = 13.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.414213562, 13.585786438}
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