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Simplifying 0 = x2 + -45x + -621 Reorder the terms: 0 = -621 + -45x + x2 Solving 0 = -621 + -45x + x2 Solving for variable 'x'. Combine like terms: 0 + 621 = 621 621 + 45x + -1x2 = -621 + -45x + x2 + 621 + 45x + -1x2 Reorder the terms: 621 + 45x + -1x2 = -621 + 621 + -45x + 45x + x2 + -1x2 Combine like terms: -621 + 621 = 0 621 + 45x + -1x2 = 0 + -45x + 45x + x2 + -1x2 621 + 45x + -1x2 = -45x + 45x + x2 + -1x2 Combine like terms: -45x + 45x = 0 621 + 45x + -1x2 = 0 + x2 + -1x2 621 + 45x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 621 + 45x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -621 + -45x + x2 = 0 Move the constant term to the right: Add '621' to each side of the equation. -621 + -45x + 621 + x2 = 0 + 621 Reorder the terms: -621 + 621 + -45x + x2 = 0 + 621 Combine like terms: -621 + 621 = 0 0 + -45x + x2 = 0 + 621 -45x + x2 = 0 + 621 Combine like terms: 0 + 621 = 621 -45x + x2 = 621 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 = 621 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 621 + 506.25 Combine like terms: 621 + 506.25 = 1127.25 506.25 + -45x + x2 = 1127.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 1127.25 Calculate the square root of the right side: 33.574543928 Break this problem into two subproblems by setting (x + -22.5) equal to 33.574543928 and -33.574543928.Subproblem 1
x + -22.5 = 33.574543928 Simplifying x + -22.5 = 33.574543928 Reorder the terms: -22.5 + x = 33.574543928 Solving -22.5 + x = 33.574543928 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 = 33.574543928 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 33.574543928 + 22.5 x = 33.574543928 + 22.5 Combine like terms: 33.574543928 + 22.5 = 56.074543928 x = 56.074543928 Simplifying x = 56.074543928Subproblem 2
x + -22.5 = -33.574543928 Simplifying x + -22.5 = -33.574543928 Reorder the terms: -22.5 + x = -33.574543928 Solving -22.5 + x = -33.574543928 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 = -33.574543928 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -33.574543928 + 22.5 x = -33.574543928 + 22.5 Combine like terms: -33.574543928 + 22.5 = -11.074543928 x = -11.074543928 Simplifying x = -11.074543928Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.074543928, -11.074543928}
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