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Simplifying 5X2 = 40X + -16 Reorder the terms: 5X2 = -16 + 40X Solving 5X2 = -16 + 40X Solving for variable 'X'. Reorder the terms: 16 + -40X + 5X2 = -16 + 40X + 16 + -40X Reorder the terms: 16 + -40X + 5X2 = -16 + 16 + 40X + -40X Combine like terms: -16 + 16 = 0 16 + -40X + 5X2 = 0 + 40X + -40X 16 + -40X + 5X2 = 40X + -40X Combine like terms: 40X + -40X = 0 16 + -40X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -8X + X2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -8X + -3.2 + X2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -8X + X2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -8X + X2 = 0 + -3.2 -8X + X2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -8X + X2 = -3.2 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = -3.2 + 16 Reorder the terms: 16 + -8X + X2 = -3.2 + 16 Combine like terms: -3.2 + 16 = 12.8 16 + -8X + X2 = 12.8 Factor a perfect square on the left side: (X + -4)(X + -4) = 12.8 Calculate the square root of the right side: 3.577708764 Break this problem into two subproblems by setting (X + -4) equal to 3.577708764 and -3.577708764.Subproblem 1
X + -4 = 3.577708764 Simplifying X + -4 = 3.577708764 Reorder the terms: -4 + X = 3.577708764 Solving -4 + X = 3.577708764 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 3.577708764 + 4 Combine like terms: -4 + 4 = 0 0 + X = 3.577708764 + 4 X = 3.577708764 + 4 Combine like terms: 3.577708764 + 4 = 7.577708764 X = 7.577708764 Simplifying X = 7.577708764Subproblem 2
X + -4 = -3.577708764 Simplifying X + -4 = -3.577708764 Reorder the terms: -4 + X = -3.577708764 Solving -4 + X = -3.577708764 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -3.577708764 + 4 Combine like terms: -4 + 4 = 0 0 + X = -3.577708764 + 4 X = -3.577708764 + 4 Combine like terms: -3.577708764 + 4 = 0.422291236 X = 0.422291236 Simplifying X = 0.422291236Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.577708764, 0.422291236}
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