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Simplifying x2 + -10x + -556 = 6 Reorder the terms: -556 + -10x + x2 = 6 Solving -556 + -10x + x2 = 6 Solving for variable 'x'. Reorder the terms: -556 + -6 + -10x + x2 = 6 + -6 Combine like terms: -556 + -6 = -562 -562 + -10x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -562 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '562' to each side of the equation. -562 + -10x + 562 + x2 = 0 + 562 Reorder the terms: -562 + 562 + -10x + x2 = 0 + 562 Combine like terms: -562 + 562 = 0 0 + -10x + x2 = 0 + 562 -10x + x2 = 0 + 562 Combine like terms: 0 + 562 = 562 -10x + x2 = 562 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 562 + 25 Reorder the terms: 25 + -10x + x2 = 562 + 25 Combine like terms: 562 + 25 = 587 25 + -10x + x2 = 587 Factor a perfect square on the left side: (x + -5)(x + -5) = 587 Calculate the square root of the right side: 24.228082879 Break this problem into two subproblems by setting (x + -5) equal to 24.228082879 and -24.228082879.Subproblem 1
x + -5 = 24.228082879 Simplifying x + -5 = 24.228082879 Reorder the terms: -5 + x = 24.228082879 Solving -5 + x = 24.228082879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 24.228082879 + 5 Combine like terms: -5 + 5 = 0 0 + x = 24.228082879 + 5 x = 24.228082879 + 5 Combine like terms: 24.228082879 + 5 = 29.228082879 x = 29.228082879 Simplifying x = 29.228082879Subproblem 2
x + -5 = -24.228082879 Simplifying x + -5 = -24.228082879 Reorder the terms: -5 + x = -24.228082879 Solving -5 + x = -24.228082879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -24.228082879 + 5 Combine like terms: -5 + 5 = 0 0 + x = -24.228082879 + 5 x = -24.228082879 + 5 Combine like terms: -24.228082879 + 5 = -19.228082879 x = -19.228082879 Simplifying x = -19.228082879Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.228082879, -19.228082879}
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