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Simplifying x2 + 76x + -1444 = 0 Reorder the terms: -1444 + 76x + x2 = 0 Solving -1444 + 76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1444' to each side of the equation. -1444 + 76x + 1444 + x2 = 0 + 1444 Reorder the terms: -1444 + 1444 + 76x + x2 = 0 + 1444 Combine like terms: -1444 + 1444 = 0 0 + 76x + x2 = 0 + 1444 76x + x2 = 0 + 1444 Combine like terms: 0 + 1444 = 1444 76x + x2 = 1444 The x term is 76x. Take half its coefficient (38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. 76x + 1444 + x2 = 1444 + 1444 Reorder the terms: 1444 + 76x + x2 = 1444 + 1444 Combine like terms: 1444 + 1444 = 2888 1444 + 76x + x2 = 2888 Factor a perfect square on the left side: (x + 38)(x + 38) = 2888 Calculate the square root of the right side: 53.74011537 Break this problem into two subproblems by setting (x + 38) equal to 53.74011537 and -53.74011537.Subproblem 1
x + 38 = 53.74011537 Simplifying x + 38 = 53.74011537 Reorder the terms: 38 + x = 53.74011537 Solving 38 + x = 53.74011537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 53.74011537 + -38 Combine like terms: 38 + -38 = 0 0 + x = 53.74011537 + -38 x = 53.74011537 + -38 Combine like terms: 53.74011537 + -38 = 15.74011537 x = 15.74011537 Simplifying x = 15.74011537Subproblem 2
x + 38 = -53.74011537 Simplifying x + 38 = -53.74011537 Reorder the terms: 38 + x = -53.74011537 Solving 38 + x = -53.74011537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = -53.74011537 + -38 Combine like terms: 38 + -38 = 0 0 + x = -53.74011537 + -38 x = -53.74011537 + -38 Combine like terms: -53.74011537 + -38 = -91.74011537 x = -91.74011537 Simplifying x = -91.74011537Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.74011537, -91.74011537}
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