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Simplifying x2 + 52x + -3000 = 0 Reorder the terms: -3000 + 52x + x2 = 0 Solving -3000 + 52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 52x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 52x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 52x + x2 = 0 + 3000 52x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 52x + x2 = 3000 The x term is 52x. Take half its coefficient (26). Square it (676) and add it to both sides. Add '676' to each side of the equation. 52x + 676 + x2 = 3000 + 676 Reorder the terms: 676 + 52x + x2 = 3000 + 676 Combine like terms: 3000 + 676 = 3676 676 + 52x + x2 = 3676 Factor a perfect square on the left side: (x + 26)(x + 26) = 3676 Calculate the square root of the right side: 60.630025565 Break this problem into two subproblems by setting (x + 26) equal to 60.630025565 and -60.630025565.Subproblem 1
x + 26 = 60.630025565 Simplifying x + 26 = 60.630025565 Reorder the terms: 26 + x = 60.630025565 Solving 26 + x = 60.630025565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = 60.630025565 + -26 Combine like terms: 26 + -26 = 0 0 + x = 60.630025565 + -26 x = 60.630025565 + -26 Combine like terms: 60.630025565 + -26 = 34.630025565 x = 34.630025565 Simplifying x = 34.630025565Subproblem 2
x + 26 = -60.630025565 Simplifying x + 26 = -60.630025565 Reorder the terms: 26 + x = -60.630025565 Solving 26 + x = -60.630025565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = -60.630025565 + -26 Combine like terms: 26 + -26 = 0 0 + x = -60.630025565 + -26 x = -60.630025565 + -26 Combine like terms: -60.630025565 + -26 = -86.630025565 x = -86.630025565 Simplifying x = -86.630025565Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.630025565, -86.630025565}
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