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Simplifying 0 = -16X2 + 96X + 10 Reorder the terms: 0 = 10 + 96X + -16X2 Solving 0 = 10 + 96X + -16X2 Solving for variable 'X'. Combine like terms: 0 + -10 = -10 -10 + -96X + 16X2 = 10 + 96X + -16X2 + -10 + -96X + 16X2 Reorder the terms: -10 + -96X + 16X2 = 10 + -10 + 96X + -96X + -16X2 + 16X2 Combine like terms: 10 + -10 = 0 -10 + -96X + 16X2 = 0 + 96X + -96X + -16X2 + 16X2 -10 + -96X + 16X2 = 96X + -96X + -16X2 + 16X2 Combine like terms: 96X + -96X = 0 -10 + -96X + 16X2 = 0 + -16X2 + 16X2 -10 + -96X + 16X2 = -16X2 + 16X2 Combine like terms: -16X2 + 16X2 = 0 -10 + -96X + 16X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -48X + 8X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -48X + 8X2)' equal to zero and attempt to solve: Simplifying -5 + -48X + 8X2 = 0 Solving -5 + -48X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -6X + X2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -6X + 0.625 + X2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -6X + X2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -6X + X2 = 0 + 0.625 -6X + X2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -6X + X2 = 0.625 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 0.625 + 9 Reorder the terms: 9 + -6X + X2 = 0.625 + 9 Combine like terms: 0.625 + 9 = 9.625 9 + -6X + X2 = 9.625 Factor a perfect square on the left side: (X + -3)(X + -3) = 9.625 Calculate the square root of the right side: 3.102418411 Break this problem into two subproblems by setting (X + -3) equal to 3.102418411 and -3.102418411.Subproblem 1
X + -3 = 3.102418411 Simplifying X + -3 = 3.102418411 Reorder the terms: -3 + X = 3.102418411 Solving -3 + X = 3.102418411 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 3.102418411 + 3 Combine like terms: -3 + 3 = 0 0 + X = 3.102418411 + 3 X = 3.102418411 + 3 Combine like terms: 3.102418411 + 3 = 6.102418411 X = 6.102418411 Simplifying X = 6.102418411Subproblem 2
X + -3 = -3.102418411 Simplifying X + -3 = -3.102418411 Reorder the terms: -3 + X = -3.102418411 Solving -3 + X = -3.102418411 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -3.102418411 + 3 Combine like terms: -3 + 3 = 0 0 + X = -3.102418411 + 3 X = -3.102418411 + 3 Combine like terms: -3.102418411 + 3 = -0.102418411 X = -0.102418411 Simplifying X = -0.102418411Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.102418411, -0.102418411}Solution
X = {6.102418411, -0.102418411}
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