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Simplifying x2 + 130x + -5775 = 1 Reorder the terms: -5775 + 130x + x2 = 1 Solving -5775 + 130x + x2 = 1 Solving for variable 'x'. Reorder the terms: -5775 + -1 + 130x + x2 = 1 + -1 Combine like terms: -5775 + -1 = -5776 -5776 + 130x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -5776 + 130x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5776' to each side of the equation. -5776 + 130x + 5776 + x2 = 0 + 5776 Reorder the terms: -5776 + 5776 + 130x + x2 = 0 + 5776 Combine like terms: -5776 + 5776 = 0 0 + 130x + x2 = 0 + 5776 130x + x2 = 0 + 5776 Combine like terms: 0 + 5776 = 5776 130x + x2 = 5776 The x term is 130x. Take half its coefficient (65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. 130x + 4225 + x2 = 5776 + 4225 Reorder the terms: 4225 + 130x + x2 = 5776 + 4225 Combine like terms: 5776 + 4225 = 10001 4225 + 130x + x2 = 10001 Factor a perfect square on the left side: (x + 65)(x + 65) = 10001 Calculate the square root of the right side: 100.004999875 Break this problem into two subproblems by setting (x + 65) equal to 100.004999875 and -100.004999875.Subproblem 1
x + 65 = 100.004999875 Simplifying x + 65 = 100.004999875 Reorder the terms: 65 + x = 100.004999875 Solving 65 + x = 100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = 100.004999875 + -65 Combine like terms: 65 + -65 = 0 0 + x = 100.004999875 + -65 x = 100.004999875 + -65 Combine like terms: 100.004999875 + -65 = 35.004999875 x = 35.004999875 Simplifying x = 35.004999875Subproblem 2
x + 65 = -100.004999875 Simplifying x + 65 = -100.004999875 Reorder the terms: 65 + x = -100.004999875 Solving 65 + x = -100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = -100.004999875 + -65 Combine like terms: 65 + -65 = 0 0 + x = -100.004999875 + -65 x = -100.004999875 + -65 Combine like terms: -100.004999875 + -65 = -165.004999875 x = -165.004999875 Simplifying x = -165.004999875Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.004999875, -165.004999875}
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