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Simplifying x2 + -146x + 520 = 0 Reorder the terms: 520 + -146x + x2 = 0 Solving 520 + -146x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-520' to each side of the equation. 520 + -146x + -520 + x2 = 0 + -520 Reorder the terms: 520 + -520 + -146x + x2 = 0 + -520 Combine like terms: 520 + -520 = 0 0 + -146x + x2 = 0 + -520 -146x + x2 = 0 + -520 Combine like terms: 0 + -520 = -520 -146x + x2 = -520 The x term is -146x. Take half its coefficient (-73). Square it (5329) and add it to both sides. Add '5329' to each side of the equation. -146x + 5329 + x2 = -520 + 5329 Reorder the terms: 5329 + -146x + x2 = -520 + 5329 Combine like terms: -520 + 5329 = 4809 5329 + -146x + x2 = 4809 Factor a perfect square on the left side: (x + -73)(x + -73) = 4809 Calculate the square root of the right side: 69.34695379 Break this problem into two subproblems by setting (x + -73) equal to 69.34695379 and -69.34695379.Subproblem 1
x + -73 = 69.34695379 Simplifying x + -73 = 69.34695379 Reorder the terms: -73 + x = 69.34695379 Solving -73 + x = 69.34695379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = 69.34695379 + 73 Combine like terms: -73 + 73 = 0 0 + x = 69.34695379 + 73 x = 69.34695379 + 73 Combine like terms: 69.34695379 + 73 = 142.34695379 x = 142.34695379 Simplifying x = 142.34695379Subproblem 2
x + -73 = -69.34695379 Simplifying x + -73 = -69.34695379 Reorder the terms: -73 + x = -69.34695379 Solving -73 + x = -69.34695379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73' to each side of the equation. -73 + 73 + x = -69.34695379 + 73 Combine like terms: -73 + 73 = 0 0 + x = -69.34695379 + 73 x = -69.34695379 + 73 Combine like terms: -69.34695379 + 73 = 3.65304621 x = 3.65304621 Simplifying x = 3.65304621Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.34695379, 3.65304621}
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