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Simplifying 0 = -16(X2) + (120X) + 25 Reorder the terms: 0 = 25 + (120X) + -16X2 Solving 0 = 25 + (120X) + -16X2 Solving for variable 'X'. Combine like terms: 0 + -25 = -25 -25 + (-120X) + 16X2 = 25 + (120X) + -16X2 + -25 + (-120X) + 16X2 Reorder the terms: -25 + (-120X) + 16X2 = 25 + -25 + (120X) + (-120X) + -16X2 + 16X2 Combine like terms: 25 + -25 = 0 -25 + (-120X) + 16X2 = 0 + (120X) + (-120X) + -16X2 + 16X2 -25 + (-120X) + 16X2 = (120X) + (-120X) + -16X2 + 16X2 Combine like terms: (120X) + (-120X) = 0 -25 + (-120X) + 16X2 = 0 + -16X2 + 16X2 -25 + (-120X) + 16X2 = -16X2 + 16X2 Combine like terms: -16X2 + 16X2 = 0 -25 + (-120X) + 16X2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + (-7.5X) + X2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + (-7.5X) + 1.5625 + X2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + (-7.5X) + X2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + (-7.5X) + X2 = 0 + 1.5625 (-7.5X) + X2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 (-7.5X) + X2 = 1.5625 The X term is (-7.5X). Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. (-7.5X) + 14.0625 + X2 = 1.5625 + 14.0625 Reorder the terms: 14.0625 + (-7.5X) + X2 = 1.5625 + 14.0625 Combine like terms: 1.5625 + 14.0625 = 15.625 14.0625 + (-7.5X) + X2 = 15.625 Factor a perfect square on the left side: (X + -3.75)(X + -3.75) = 15.625 Calculate the square root of the right side: 3.952847075 Break this problem into two subproblems by setting (X + -3.75) equal to 3.952847075 and -3.952847075.Subproblem 1
X + -3.75 = 3.952847075 Simplifying X + -3.75 = 3.952847075 Reorder the terms: -3.75 + X = 3.952847075 Solving -3.75 + X = 3.952847075 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = 3.952847075 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = 3.952847075 + 3.75 X = 3.952847075 + 3.75 Combine like terms: 3.952847075 + 3.75 = 7.702847075 X = 7.702847075 Simplifying X = 7.702847075Subproblem 2
X + -3.75 = -3.952847075 Simplifying X + -3.75 = -3.952847075 Reorder the terms: -3.75 + X = -3.952847075 Solving -3.75 + X = -3.952847075 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = -3.952847075 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = -3.952847075 + 3.75 X = -3.952847075 + 3.75 Combine like terms: -3.952847075 + 3.75 = -0.202847075 X = -0.202847075 Simplifying X = -0.202847075Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.702847075, -0.202847075}
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