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Simplifying x2 + -320 = x + -10 Reorder the terms: -320 + x2 = x + -10 Reorder the terms: -320 + x2 = -10 + x Solving -320 + x2 = -10 + x Solving for variable 'x'. Reorder the terms: -320 + 10 + -1x + x2 = -10 + x + 10 + -1x Combine like terms: -320 + 10 = -310 -310 + -1x + x2 = -10 + x + 10 + -1x Reorder the terms: -310 + -1x + x2 = -10 + 10 + x + -1x Combine like terms: -10 + 10 = 0 -310 + -1x + x2 = 0 + x + -1x -310 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -310 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '310' to each side of the equation. -310 + -1x + 310 + x2 = 0 + 310 Reorder the terms: -310 + 310 + -1x + x2 = 0 + 310 Combine like terms: -310 + 310 = 0 0 + -1x + x2 = 0 + 310 -1x + x2 = 0 + 310 Combine like terms: 0 + 310 = 310 -1x + x2 = 310 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 310 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 310 + 0.25 Combine like terms: 310 + 0.25 = 310.25 0.25 + -1x + x2 = 310.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 310.25 Calculate the square root of the right side: 17.613914954 Break this problem into two subproblems by setting (x + -0.5) equal to 17.613914954 and -17.613914954.Subproblem 1
x + -0.5 = 17.613914954 Simplifying x + -0.5 = 17.613914954 Reorder the terms: -0.5 + x = 17.613914954 Solving -0.5 + x = 17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 17.613914954 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 17.613914954 + 0.5 x = 17.613914954 + 0.5 Combine like terms: 17.613914954 + 0.5 = 18.113914954 x = 18.113914954 Simplifying x = 18.113914954Subproblem 2
x + -0.5 = -17.613914954 Simplifying x + -0.5 = -17.613914954 Reorder the terms: -0.5 + x = -17.613914954 Solving -0.5 + x = -17.613914954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -17.613914954 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -17.613914954 + 0.5 x = -17.613914954 + 0.5 Combine like terms: -17.613914954 + 0.5 = -17.113914954 x = -17.113914954 Simplifying x = -17.113914954Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.113914954, -17.113914954}
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