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Simplifying x2 + -72x + -3770 = 0 Reorder the terms: -3770 + -72x + x2 = 0 Solving -3770 + -72x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3770' to each side of the equation. -3770 + -72x + 3770 + x2 = 0 + 3770 Reorder the terms: -3770 + 3770 + -72x + x2 = 0 + 3770 Combine like terms: -3770 + 3770 = 0 0 + -72x + x2 = 0 + 3770 -72x + x2 = 0 + 3770 Combine like terms: 0 + 3770 = 3770 -72x + x2 = 3770 The x term is -72x. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72x + 1296 + x2 = 3770 + 1296 Reorder the terms: 1296 + -72x + x2 = 3770 + 1296 Combine like terms: 3770 + 1296 = 5066 1296 + -72x + x2 = 5066 Factor a perfect square on the left side: (x + -36)(x + -36) = 5066 Calculate the square root of the right side: 71.175838597 Break this problem into two subproblems by setting (x + -36) equal to 71.175838597 and -71.175838597.Subproblem 1
x + -36 = 71.175838597 Simplifying x + -36 = 71.175838597 Reorder the terms: -36 + x = 71.175838597 Solving -36 + x = 71.175838597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 71.175838597 + 36 Combine like terms: -36 + 36 = 0 0 + x = 71.175838597 + 36 x = 71.175838597 + 36 Combine like terms: 71.175838597 + 36 = 107.175838597 x = 107.175838597 Simplifying x = 107.175838597Subproblem 2
x + -36 = -71.175838597 Simplifying x + -36 = -71.175838597 Reorder the terms: -36 + x = -71.175838597 Solving -36 + x = -71.175838597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -71.175838597 + 36 Combine like terms: -36 + 36 = 0 0 + x = -71.175838597 + 36 x = -71.175838597 + 36 Combine like terms: -71.175838597 + 36 = -35.175838597 x = -35.175838597 Simplifying x = -35.175838597Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.175838597, -35.175838597}
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