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Simplifying 0 = X2 + 10X + -900 Reorder the terms: 0 = -900 + 10X + X2 Solving 0 = -900 + 10X + X2 Solving for variable 'X'. Combine like terms: 0 + 900 = 900 900 + -10X + -1X2 = -900 + 10X + X2 + 900 + -10X + -1X2 Reorder the terms: 900 + -10X + -1X2 = -900 + 900 + 10X + -10X + X2 + -1X2 Combine like terms: -900 + 900 = 0 900 + -10X + -1X2 = 0 + 10X + -10X + X2 + -1X2 900 + -10X + -1X2 = 10X + -10X + X2 + -1X2 Combine like terms: 10X + -10X = 0 900 + -10X + -1X2 = 0 + X2 + -1X2 900 + -10X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 900 + -10X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -900 + 10X + X2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 10X + 900 + X2 = 0 + 900 Reorder the terms: -900 + 900 + 10X + X2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 10X + X2 = 0 + 900 10X + X2 = 0 + 900 Combine like terms: 0 + 900 = 900 10X + X2 = 900 The X term is 10X. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10X + 25 + X2 = 900 + 25 Reorder the terms: 25 + 10X + X2 = 900 + 25 Combine like terms: 900 + 25 = 925 25 + 10X + X2 = 925 Factor a perfect square on the left side: (X + 5)(X + 5) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (X + 5) equal to 30.413812651 and -30.413812651.Subproblem 1
X + 5 = 30.413812651 Simplifying X + 5 = 30.413812651 Reorder the terms: 5 + X = 30.413812651 Solving 5 + X = 30.413812651 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 30.413812651 + -5 Combine like terms: 5 + -5 = 0 0 + X = 30.413812651 + -5 X = 30.413812651 + -5 Combine like terms: 30.413812651 + -5 = 25.413812651 X = 25.413812651 Simplifying X = 25.413812651Subproblem 2
X + 5 = -30.413812651 Simplifying X + 5 = -30.413812651 Reorder the terms: 5 + X = -30.413812651 Solving 5 + X = -30.413812651 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = -30.413812651 + -5 Combine like terms: 5 + -5 = 0 0 + X = -30.413812651 + -5 X = -30.413812651 + -5 Combine like terms: -30.413812651 + -5 = -35.413812651 X = -35.413812651 Simplifying X = -35.413812651Solution
The solution to the problem is based on the solutions from the subproblems. X = {25.413812651, -35.413812651}
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