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Simplifying 39x2 + -498x + -2430 = 0 Reorder the terms: -2430 + -498x + 39x2 = 0 Solving -2430 + -498x + 39x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-810 + -166x + 13x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-810 + -166x + 13x2)' equal to zero and attempt to solve: Simplifying -810 + -166x + 13x2 = 0 Solving -810 + -166x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -62.30769231 + -12.76923077x + x2 = 0 Move the constant term to the right: Add '62.30769231' to each side of the equation. -62.30769231 + -12.76923077x + 62.30769231 + x2 = 0 + 62.30769231 Reorder the terms: -62.30769231 + 62.30769231 + -12.76923077x + x2 = 0 + 62.30769231 Combine like terms: -62.30769231 + 62.30769231 = 0.00000000 0.00000000 + -12.76923077x + x2 = 0 + 62.30769231 -12.76923077x + x2 = 0 + 62.30769231 Combine like terms: 0 + 62.30769231 = 62.30769231 -12.76923077x + x2 = 62.30769231 The x term is -12.76923077x. Take half its coefficient (-6.384615385). Square it (40.76331361) and add it to both sides. Add '40.76331361' to each side of the equation. -12.76923077x + 40.76331361 + x2 = 62.30769231 + 40.76331361 Reorder the terms: 40.76331361 + -12.76923077x + x2 = 62.30769231 + 40.76331361 Combine like terms: 62.30769231 + 40.76331361 = 103.07100592 40.76331361 + -12.76923077x + x2 = 103.07100592 Factor a perfect square on the left side: (x + -6.384615385)(x + -6.384615385) = 103.07100592 Calculate the square root of the right side: 10.152389173 Break this problem into two subproblems by setting (x + -6.384615385) equal to 10.152389173 and -10.152389173.Subproblem 1
x + -6.384615385 = 10.152389173 Simplifying x + -6.384615385 = 10.152389173 Reorder the terms: -6.384615385 + x = 10.152389173 Solving -6.384615385 + x = 10.152389173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.384615385' to each side of the equation. -6.384615385 + 6.384615385 + x = 10.152389173 + 6.384615385 Combine like terms: -6.384615385 + 6.384615385 = 0.000000000 0.000000000 + x = 10.152389173 + 6.384615385 x = 10.152389173 + 6.384615385 Combine like terms: 10.152389173 + 6.384615385 = 16.537004558 x = 16.537004558 Simplifying x = 16.537004558Subproblem 2
x + -6.384615385 = -10.152389173 Simplifying x + -6.384615385 = -10.152389173 Reorder the terms: -6.384615385 + x = -10.152389173 Solving -6.384615385 + x = -10.152389173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.384615385' to each side of the equation. -6.384615385 + 6.384615385 + x = -10.152389173 + 6.384615385 Combine like terms: -6.384615385 + 6.384615385 = 0.000000000 0.000000000 + x = -10.152389173 + 6.384615385 x = -10.152389173 + 6.384615385 Combine like terms: -10.152389173 + 6.384615385 = -3.767773788 x = -3.767773788 Simplifying x = -3.767773788Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.537004558, -3.767773788}Solution
x = {16.537004558, -3.767773788}
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