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Simplifying x2 + 48x + -3000 = 0 Reorder the terms: -3000 + 48x + x2 = 0 Solving -3000 + 48x + 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 + 48x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 48x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 48x + x2 = 0 + 3000 48x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 48x + x2 = 3000 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = 3000 + 576 Reorder the terms: 576 + 48x + x2 = 3000 + 576 Combine like terms: 3000 + 576 = 3576 576 + 48x + x2 = 3576 Factor a perfect square on the left side: (x + 24)(x + 24) = 3576 Calculate the square root of the right side: 59.799665551 Break this problem into two subproblems by setting (x + 24) equal to 59.799665551 and -59.799665551.Subproblem 1
x + 24 = 59.799665551 Simplifying x + 24 = 59.799665551 Reorder the terms: 24 + x = 59.799665551 Solving 24 + x = 59.799665551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 59.799665551 + -24 Combine like terms: 24 + -24 = 0 0 + x = 59.799665551 + -24 x = 59.799665551 + -24 Combine like terms: 59.799665551 + -24 = 35.799665551 x = 35.799665551 Simplifying x = 35.799665551Subproblem 2
x + 24 = -59.799665551 Simplifying x + 24 = -59.799665551 Reorder the terms: 24 + x = -59.799665551 Solving 24 + x = -59.799665551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -59.799665551 + -24 Combine like terms: 24 + -24 = 0 0 + x = -59.799665551 + -24 x = -59.799665551 + -24 Combine like terms: -59.799665551 + -24 = -83.799665551 x = -83.799665551 Simplifying x = -83.799665551Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.799665551, -83.799665551}
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