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Simplifying 96x2 + -204x + -99 = 0 Reorder the terms: -99 + -204x + 96x2 = 0 Solving -99 + -204x + 96x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -68x + 32x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-33 + -68x + 32x2)' equal to zero and attempt to solve: Simplifying -33 + -68x + 32x2 = 0 Solving -33 + -68x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.03125 + -2.125x + x2 = 0 Move the constant term to the right: Add '1.03125' to each side of the equation. -1.03125 + -2.125x + 1.03125 + x2 = 0 + 1.03125 Reorder the terms: -1.03125 + 1.03125 + -2.125x + x2 = 0 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + -2.125x + x2 = 0 + 1.03125 -2.125x + x2 = 0 + 1.03125 Combine like terms: 0 + 1.03125 = 1.03125 -2.125x + x2 = 1.03125 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 1.03125 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 1.03125 + 1.12890625 Combine like terms: 1.03125 + 1.12890625 = 2.16015625 1.12890625 + -2.125x + x2 = 2.16015625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 2.16015625 Calculate the square root of the right side: 1.469747002 Break this problem into two subproblems by setting (x + -1.0625) equal to 1.469747002 and -1.469747002.Subproblem 1
x + -1.0625 = 1.469747002 Simplifying x + -1.0625 = 1.469747002 Reorder the terms: -1.0625 + x = 1.469747002 Solving -1.0625 + x = 1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 1.469747002 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 1.469747002 + 1.0625 x = 1.469747002 + 1.0625 Combine like terms: 1.469747002 + 1.0625 = 2.532247002 x = 2.532247002 Simplifying x = 2.532247002Subproblem 2
x + -1.0625 = -1.469747002 Simplifying x + -1.0625 = -1.469747002 Reorder the terms: -1.0625 + x = -1.469747002 Solving -1.0625 + x = -1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -1.469747002 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -1.469747002 + 1.0625 x = -1.469747002 + 1.0625 Combine like terms: -1.469747002 + 1.0625 = -0.407247002 x = -0.407247002 Simplifying x = -0.407247002Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.532247002, -0.407247002}Solution
x = {2.532247002, -0.407247002}
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