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Simplifying x2 + 45x + -1350 = 0 Reorder the terms: -1350 + 45x + x2 = 0 Solving -1350 + 45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1350' to each side of the equation. -1350 + 45x + 1350 + x2 = 0 + 1350 Reorder the terms: -1350 + 1350 + 45x + x2 = 0 + 1350 Combine like terms: -1350 + 1350 = 0 0 + 45x + x2 = 0 + 1350 45x + x2 = 0 + 1350 Combine like terms: 0 + 1350 = 1350 45x + x2 = 1350 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 1350 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 1350 + 506.25 Combine like terms: 1350 + 506.25 = 1856.25 506.25 + 45x + x2 = 1856.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 1856.25 Calculate the square root of the right side: 43.084219849 Break this problem into two subproblems by setting (x + 22.5) equal to 43.084219849 and -43.084219849.Subproblem 1
x + 22.5 = 43.084219849 Simplifying x + 22.5 = 43.084219849 Reorder the terms: 22.5 + x = 43.084219849 Solving 22.5 + x = 43.084219849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 43.084219849 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 43.084219849 + -22.5 x = 43.084219849 + -22.5 Combine like terms: 43.084219849 + -22.5 = 20.584219849 x = 20.584219849 Simplifying x = 20.584219849Subproblem 2
x + 22.5 = -43.084219849 Simplifying x + 22.5 = -43.084219849 Reorder the terms: 22.5 + x = -43.084219849 Solving 22.5 + x = -43.084219849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -43.084219849 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -43.084219849 + -22.5 x = -43.084219849 + -22.5 Combine like terms: -43.084219849 + -22.5 = -65.584219849 x = -65.584219849 Simplifying x = -65.584219849Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.584219849, -65.584219849}
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