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Simplifying 2175x2 + 5955x + 5255 = 90000 Reorder the terms: 5255 + 5955x + 2175x2 = 90000 Solving 5255 + 5955x + 2175x2 = 90000 Solving for variable 'x'. Reorder the terms: 5255 + -90000 + 5955x + 2175x2 = 90000 + -90000 Combine like terms: 5255 + -90000 = -84745 -84745 + 5955x + 2175x2 = 90000 + -90000 Combine like terms: 90000 + -90000 = 0 -84745 + 5955x + 2175x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16949 + 1191x + 435x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16949 + 1191x + 435x2)' equal to zero and attempt to solve: Simplifying -16949 + 1191x + 435x2 = 0 Solving -16949 + 1191x + 435x2 = 0 Begin completing the square. Divide all terms by 435 the coefficient of the squared term: Divide each side by '435'. -38.96321839 + 2.737931034x + x2 = 0 Move the constant term to the right: Add '38.96321839' to each side of the equation. -38.96321839 + 2.737931034x + 38.96321839 + x2 = 0 + 38.96321839 Reorder the terms: -38.96321839 + 38.96321839 + 2.737931034x + x2 = 0 + 38.96321839 Combine like terms: -38.96321839 + 38.96321839 = 0.00000000 0.00000000 + 2.737931034x + x2 = 0 + 38.96321839 2.737931034x + x2 = 0 + 38.96321839 Combine like terms: 0 + 38.96321839 = 38.96321839 2.737931034x + x2 = 38.96321839 The x term is 2.737931034x. Take half its coefficient (1.368965517). Square it (1.874066587) and add it to both sides. Add '1.874066587' to each side of the equation. 2.737931034x + 1.874066587 + x2 = 38.96321839 + 1.874066587 Reorder the terms: 1.874066587 + 2.737931034x + x2 = 38.96321839 + 1.874066587 Combine like terms: 38.96321839 + 1.874066587 = 40.837284977 1.874066587 + 2.737931034x + x2 = 40.837284977 Factor a perfect square on the left side: (x + 1.368965517)(x + 1.368965517) = 40.837284977 Calculate the square root of the right side: 6.390405697 Break this problem into two subproblems by setting (x + 1.368965517) equal to 6.390405697 and -6.390405697.Subproblem 1
x + 1.368965517 = 6.390405697 Simplifying x + 1.368965517 = 6.390405697 Reorder the terms: 1.368965517 + x = 6.390405697 Solving 1.368965517 + x = 6.390405697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.368965517' to each side of the equation. 1.368965517 + -1.368965517 + x = 6.390405697 + -1.368965517 Combine like terms: 1.368965517 + -1.368965517 = 0.000000000 0.000000000 + x = 6.390405697 + -1.368965517 x = 6.390405697 + -1.368965517 Combine like terms: 6.390405697 + -1.368965517 = 5.02144018 x = 5.02144018 Simplifying x = 5.02144018Subproblem 2
x + 1.368965517 = -6.390405697 Simplifying x + 1.368965517 = -6.390405697 Reorder the terms: 1.368965517 + x = -6.390405697 Solving 1.368965517 + x = -6.390405697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.368965517' to each side of the equation. 1.368965517 + -1.368965517 + x = -6.390405697 + -1.368965517 Combine like terms: 1.368965517 + -1.368965517 = 0.000000000 0.000000000 + x = -6.390405697 + -1.368965517 x = -6.390405697 + -1.368965517 Combine like terms: -6.390405697 + -1.368965517 = -7.759371214 x = -7.759371214 Simplifying x = -7.759371214Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.02144018, -7.759371214}Solution
x = {5.02144018, -7.759371214}
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