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Simplifying 0 = -16(X2) + (120X) + 100 Reorder the terms: 0 = 100 + (120X) + -16X2 Solving 0 = 100 + (120X) + -16X2 Solving for variable 'X'. Combine like terms: 0 + -100 = -100 -100 + (-120X) + 16X2 = 100 + (120X) + -16X2 + -100 + (-120X) + 16X2 Reorder the terms: -100 + (-120X) + 16X2 = 100 + -100 + (120X) + (-120X) + -16X2 + 16X2 Combine like terms: 100 + -100 = 0 -100 + (-120X) + 16X2 = 0 + (120X) + (-120X) + -16X2 + 16X2 -100 + (-120X) + 16X2 = (120X) + (-120X) + -16X2 + 16X2 Combine like terms: (120X) + (-120X) = 0 -100 + (-120X) + 16X2 = 0 + -16X2 + 16X2 -100 + (-120X) + 16X2 = -16X2 + 16X2 Combine like terms: -16X2 + 16X2 = 0 -100 + (-120X) + 16X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + (-30X) + 4X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + (-30X) + 4X2)' equal to zero and attempt to solve: Simplifying -25 + (-30X) + 4X2 = 0 Solving -25 + (-30X) + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + (-7.5X) + X2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + (-7.5X) + 6.25 + X2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + (-7.5X) + X2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + (-7.5X) + X2 = 0 + 6.25 (-7.5X) + X2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 (-7.5X) + X2 = 6.25 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 = 6.25 + 14.0625 Reorder the terms: 14.0625 + (-7.5X) + X2 = 6.25 + 14.0625 Combine like terms: 6.25 + 14.0625 = 20.3125 14.0625 + (-7.5X) + X2 = 20.3125 Factor a perfect square on the left side: (X + -3.75)(X + -3.75) = 20.3125 Calculate the square root of the right side: 4.506939094 Break this problem into two subproblems by setting (X + -3.75) equal to 4.506939094 and -4.506939094.Subproblem 1
X + -3.75 = 4.506939094 Simplifying X + -3.75 = 4.506939094 Reorder the terms: -3.75 + X = 4.506939094 Solving -3.75 + X = 4.506939094 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 = 4.506939094 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = 4.506939094 + 3.75 X = 4.506939094 + 3.75 Combine like terms: 4.506939094 + 3.75 = 8.256939094 X = 8.256939094 Simplifying X = 8.256939094Subproblem 2
X + -3.75 = -4.506939094 Simplifying X + -3.75 = -4.506939094 Reorder the terms: -3.75 + X = -4.506939094 Solving -3.75 + X = -4.506939094 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 = -4.506939094 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = -4.506939094 + 3.75 X = -4.506939094 + 3.75 Combine like terms: -4.506939094 + 3.75 = -0.756939094 X = -0.756939094 Simplifying X = -0.756939094Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.256939094, -0.756939094}Solution
X = {8.256939094, -0.756939094}
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