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Simplifying x2 + 2 = 678x + 2x + -34560 Reorder the terms: 2 + x2 = 678x + 2x + -34560 Reorder the terms: 2 + x2 = -34560 + 678x + 2x Combine like terms: 678x + 2x = 680x 2 + x2 = -34560 + 680x Solving 2 + x2 = -34560 + 680x Solving for variable 'x'. Reorder the terms: 2 + 34560 + -680x + x2 = -34560 + 680x + 34560 + -680x Combine like terms: 2 + 34560 = 34562 34562 + -680x + x2 = -34560 + 680x + 34560 + -680x Reorder the terms: 34562 + -680x + x2 = -34560 + 34560 + 680x + -680x Combine like terms: -34560 + 34560 = 0 34562 + -680x + x2 = 0 + 680x + -680x 34562 + -680x + x2 = 680x + -680x Combine like terms: 680x + -680x = 0 34562 + -680x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-34562' to each side of the equation. 34562 + -680x + -34562 + x2 = 0 + -34562 Reorder the terms: 34562 + -34562 + -680x + x2 = 0 + -34562 Combine like terms: 34562 + -34562 = 0 0 + -680x + x2 = 0 + -34562 -680x + x2 = 0 + -34562 Combine like terms: 0 + -34562 = -34562 -680x + x2 = -34562 The x term is -680x. Take half its coefficient (-340). Square it (115600) and add it to both sides. Add '115600' to each side of the equation. -680x + 115600 + x2 = -34562 + 115600 Reorder the terms: 115600 + -680x + x2 = -34562 + 115600 Combine like terms: -34562 + 115600 = 81038 115600 + -680x + x2 = 81038 Factor a perfect square on the left side: (x + -340)(x + -340) = 81038 Calculate the square root of the right side: 284.671740782 Break this problem into two subproblems by setting (x + -340) equal to 284.671740782 and -284.671740782.Subproblem 1
x + -340 = 284.671740782 Simplifying x + -340 = 284.671740782 Reorder the terms: -340 + x = 284.671740782 Solving -340 + x = 284.671740782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '340' to each side of the equation. -340 + 340 + x = 284.671740782 + 340 Combine like terms: -340 + 340 = 0 0 + x = 284.671740782 + 340 x = 284.671740782 + 340 Combine like terms: 284.671740782 + 340 = 624.671740782 x = 624.671740782 Simplifying x = 624.671740782Subproblem 2
x + -340 = -284.671740782 Simplifying x + -340 = -284.671740782 Reorder the terms: -340 + x = -284.671740782 Solving -340 + x = -284.671740782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '340' to each side of the equation. -340 + 340 + x = -284.671740782 + 340 Combine like terms: -340 + 340 = 0 0 + x = -284.671740782 + 340 x = -284.671740782 + 340 Combine like terms: -284.671740782 + 340 = 55.328259218 x = 55.328259218 Simplifying x = 55.328259218Solution
The solution to the problem is based on the solutions from the subproblems. x = {624.671740782, 55.328259218}
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