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Simplifying 2X2 + 20X = 525 Reorder the terms: 20X + 2X2 = 525 Solving 20X + 2X2 = 525 Solving for variable 'X'. Reorder the terms: -525 + 20X + 2X2 = 525 + -525 Combine like terms: 525 + -525 = 0 -525 + 20X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -262.5 + 10X + X2 = 0 Move the constant term to the right: Add '262.5' to each side of the equation. -262.5 + 10X + 262.5 + X2 = 0 + 262.5 Reorder the terms: -262.5 + 262.5 + 10X + X2 = 0 + 262.5 Combine like terms: -262.5 + 262.5 = 0.0 0.0 + 10X + X2 = 0 + 262.5 10X + X2 = 0 + 262.5 Combine like terms: 0 + 262.5 = 262.5 10X + X2 = 262.5 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 = 262.5 + 25 Reorder the terms: 25 + 10X + X2 = 262.5 + 25 Combine like terms: 262.5 + 25 = 287.5 25 + 10X + X2 = 287.5 Factor a perfect square on the left side: (X + 5)(X + 5) = 287.5 Calculate the square root of the right side: 16.955824958 Break this problem into two subproblems by setting (X + 5) equal to 16.955824958 and -16.955824958.Subproblem 1
X + 5 = 16.955824958 Simplifying X + 5 = 16.955824958 Reorder the terms: 5 + X = 16.955824958 Solving 5 + X = 16.955824958 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 = 16.955824958 + -5 Combine like terms: 5 + -5 = 0 0 + X = 16.955824958 + -5 X = 16.955824958 + -5 Combine like terms: 16.955824958 + -5 = 11.955824958 X = 11.955824958 Simplifying X = 11.955824958Subproblem 2
X + 5 = -16.955824958 Simplifying X + 5 = -16.955824958 Reorder the terms: 5 + X = -16.955824958 Solving 5 + X = -16.955824958 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 = -16.955824958 + -5 Combine like terms: 5 + -5 = 0 0 + X = -16.955824958 + -5 X = -16.955824958 + -5 Combine like terms: -16.955824958 + -5 = -21.955824958 X = -21.955824958 Simplifying X = -21.955824958Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.955824958, -21.955824958}
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