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Simplifying 39x2 + -480x + -2460 = 0 Reorder the terms: -2460 + -480x + 39x2 = 0 Solving -2460 + -480x + 39x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-820 + -160x + 13x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-820 + -160x + 13x2)' equal to zero and attempt to solve: Simplifying -820 + -160x + 13x2 = 0 Solving -820 + -160x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -63.07692308 + -12.30769231x + x2 = 0 Move the constant term to the right: Add '63.07692308' to each side of the equation. -63.07692308 + -12.30769231x + 63.07692308 + x2 = 0 + 63.07692308 Reorder the terms: -63.07692308 + 63.07692308 + -12.30769231x + x2 = 0 + 63.07692308 Combine like terms: -63.07692308 + 63.07692308 = 0.00000000 0.00000000 + -12.30769231x + x2 = 0 + 63.07692308 -12.30769231x + x2 = 0 + 63.07692308 Combine like terms: 0 + 63.07692308 = 63.07692308 -12.30769231x + x2 = 63.07692308 The x term is -12.30769231x. Take half its coefficient (-6.153846155). Square it (37.86982250) and add it to both sides. Add '37.86982250' to each side of the equation. -12.30769231x + 37.86982250 + x2 = 63.07692308 + 37.86982250 Reorder the terms: 37.86982250 + -12.30769231x + x2 = 63.07692308 + 37.86982250 Combine like terms: 63.07692308 + 37.86982250 = 100.94674558 37.86982250 + -12.30769231x + x2 = 100.94674558 Factor a perfect square on the left side: (x + -6.153846155)(x + -6.153846155) = 100.94674558 Calculate the square root of the right side: 10.047225765 Break this problem into two subproblems by setting (x + -6.153846155) equal to 10.047225765 and -10.047225765.Subproblem 1
x + -6.153846155 = 10.047225765 Simplifying x + -6.153846155 = 10.047225765 Reorder the terms: -6.153846155 + x = 10.047225765 Solving -6.153846155 + x = 10.047225765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.153846155' to each side of the equation. -6.153846155 + 6.153846155 + x = 10.047225765 + 6.153846155 Combine like terms: -6.153846155 + 6.153846155 = 0.000000000 0.000000000 + x = 10.047225765 + 6.153846155 x = 10.047225765 + 6.153846155 Combine like terms: 10.047225765 + 6.153846155 = 16.20107192 x = 16.20107192 Simplifying x = 16.20107192Subproblem 2
x + -6.153846155 = -10.047225765 Simplifying x + -6.153846155 = -10.047225765 Reorder the terms: -6.153846155 + x = -10.047225765 Solving -6.153846155 + x = -10.047225765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.153846155' to each side of the equation. -6.153846155 + 6.153846155 + x = -10.047225765 + 6.153846155 Combine like terms: -6.153846155 + 6.153846155 = 0.000000000 0.000000000 + x = -10.047225765 + 6.153846155 x = -10.047225765 + 6.153846155 Combine like terms: -10.047225765 + 6.153846155 = -3.89337961 x = -3.89337961 Simplifying x = -3.89337961Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.20107192, -3.89337961}Solution
x = {16.20107192, -3.89337961}
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