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Simplifying 0 = 3x2 + -51x + -33 Reorder the terms: 0 = -33 + -51x + 3x2 Solving 0 = -33 + -51x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 33 = 33 33 + 51x + -3x2 = -33 + -51x + 3x2 + 33 + 51x + -3x2 Reorder the terms: 33 + 51x + -3x2 = -33 + 33 + -51x + 51x + 3x2 + -3x2 Combine like terms: -33 + 33 = 0 33 + 51x + -3x2 = 0 + -51x + 51x + 3x2 + -3x2 33 + 51x + -3x2 = -51x + 51x + 3x2 + -3x2 Combine like terms: -51x + 51x = 0 33 + 51x + -3x2 = 0 + 3x2 + -3x2 33 + 51x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 33 + 51x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + 17x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + 17x + -1x2)' equal to zero and attempt to solve: Simplifying 11 + 17x + -1x2 = 0 Solving 11 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -17x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -17x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -17x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -17x + x2 = 0 + 11 -17x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -17x + x2 = 11 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 11 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 11 + 72.25 Combine like terms: 11 + 72.25 = 83.25 72.25 + -17x + x2 = 83.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + -8.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + -8.5 = 9.124143795 Simplifying x + -8.5 = 9.124143795 Reorder the terms: -8.5 + x = 9.124143795 Solving -8.5 + x = 9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 9.124143795 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.124143795 + 8.5 x = 9.124143795 + 8.5 Combine like terms: 9.124143795 + 8.5 = 17.624143795 x = 17.624143795 Simplifying x = 17.624143795Subproblem 2
x + -8.5 = -9.124143795 Simplifying x + -8.5 = -9.124143795 Reorder the terms: -8.5 + x = -9.124143795 Solving -8.5 + x = -9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -9.124143795 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.124143795 + 8.5 x = -9.124143795 + 8.5 Combine like terms: -9.124143795 + 8.5 = -0.624143795 x = -0.624143795 Simplifying x = -0.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.624143795, -0.624143795}Solution
x = {17.624143795, -0.624143795}
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