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Simplifying 33x2 + -576x + -3456 = 0 Reorder the terms: -3456 + -576x + 33x2 = 0 Solving -3456 + -576x + 33x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1152 + -192x + 11x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1152 + -192x + 11x2)' equal to zero and attempt to solve: Simplifying -1152 + -192x + 11x2 = 0 Solving -1152 + -192x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -104.7272727 + -17.45454545x + x2 = 0 Move the constant term to the right: Add '104.7272727' to each side of the equation. -104.7272727 + -17.45454545x + 104.7272727 + x2 = 0 + 104.7272727 Reorder the terms: -104.7272727 + 104.7272727 + -17.45454545x + x2 = 0 + 104.7272727 Combine like terms: -104.7272727 + 104.7272727 = 0.0000000 0.0000000 + -17.45454545x + x2 = 0 + 104.7272727 -17.45454545x + x2 = 0 + 104.7272727 Combine like terms: 0 + 104.7272727 = 104.7272727 -17.45454545x + x2 = 104.7272727 The x term is -17.45454545x. Take half its coefficient (-8.727272725). Square it (76.16528922) and add it to both sides. Add '76.16528922' to each side of the equation. -17.45454545x + 76.16528922 + x2 = 104.7272727 + 76.16528922 Reorder the terms: 76.16528922 + -17.45454545x + x2 = 104.7272727 + 76.16528922 Combine like terms: 104.7272727 + 76.16528922 = 180.89256192 76.16528922 + -17.45454545x + x2 = 180.89256192 Factor a perfect square on the left side: (x + -8.727272725)(x + -8.727272725) = 180.89256192 Calculate the square root of the right side: 13.44963055 Break this problem into two subproblems by setting (x + -8.727272725) equal to 13.44963055 and -13.44963055.Subproblem 1
x + -8.727272725 = 13.44963055 Simplifying x + -8.727272725 = 13.44963055 Reorder the terms: -8.727272725 + x = 13.44963055 Solving -8.727272725 + x = 13.44963055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.727272725' to each side of the equation. -8.727272725 + 8.727272725 + x = 13.44963055 + 8.727272725 Combine like terms: -8.727272725 + 8.727272725 = 0.000000000 0.000000000 + x = 13.44963055 + 8.727272725 x = 13.44963055 + 8.727272725 Combine like terms: 13.44963055 + 8.727272725 = 22.176903275 x = 22.176903275 Simplifying x = 22.176903275Subproblem 2
x + -8.727272725 = -13.44963055 Simplifying x + -8.727272725 = -13.44963055 Reorder the terms: -8.727272725 + x = -13.44963055 Solving -8.727272725 + x = -13.44963055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.727272725' to each side of the equation. -8.727272725 + 8.727272725 + x = -13.44963055 + 8.727272725 Combine like terms: -8.727272725 + 8.727272725 = 0.000000000 0.000000000 + x = -13.44963055 + 8.727272725 x = -13.44963055 + 8.727272725 Combine like terms: -13.44963055 + 8.727272725 = -4.722357825 x = -4.722357825 Simplifying x = -4.722357825Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.176903275, -4.722357825}Solution
x = {22.176903275, -4.722357825}
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