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Simplifying 879x + 108x2 = 48 Solving 879x + 108x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 879x + 108x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 879x + 108x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + 293x + 36x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-16 + 293x + 36x2)' equal to zero and attempt to solve: Simplifying -16 + 293x + 36x2 = 0 Solving -16 + 293x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.4444444444 + 8.138888889x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 8.138888889x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 8.138888889x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 8.138888889x + x2 = 0 + 0.4444444444 8.138888889x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 8.138888889x + x2 = 0.4444444444 The x term is 8.138888889x. Take half its coefficient (4.069444445). Square it (16.56037809) and add it to both sides. Add '16.56037809' to each side of the equation. 8.138888889x + 16.56037809 + x2 = 0.4444444444 + 16.56037809 Reorder the terms: 16.56037809 + 8.138888889x + x2 = 0.4444444444 + 16.56037809 Combine like terms: 0.4444444444 + 16.56037809 = 17.0048225344 16.56037809 + 8.138888889x + x2 = 17.0048225344 Factor a perfect square on the left side: (x + 4.069444445)(x + 4.069444445) = 17.0048225344 Calculate the square root of the right side: 4.123690402 Break this problem into two subproblems by setting (x + 4.069444445) equal to 4.123690402 and -4.123690402.Subproblem 1
x + 4.069444445 = 4.123690402 Simplifying x + 4.069444445 = 4.123690402 Reorder the terms: 4.069444445 + x = 4.123690402 Solving 4.069444445 + x = 4.123690402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.069444445' to each side of the equation. 4.069444445 + -4.069444445 + x = 4.123690402 + -4.069444445 Combine like terms: 4.069444445 + -4.069444445 = 0.000000000 0.000000000 + x = 4.123690402 + -4.069444445 x = 4.123690402 + -4.069444445 Combine like terms: 4.123690402 + -4.069444445 = 0.054245957 x = 0.054245957 Simplifying x = 0.054245957Subproblem 2
x + 4.069444445 = -4.123690402 Simplifying x + 4.069444445 = -4.123690402 Reorder the terms: 4.069444445 + x = -4.123690402 Solving 4.069444445 + x = -4.123690402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.069444445' to each side of the equation. 4.069444445 + -4.069444445 + x = -4.123690402 + -4.069444445 Combine like terms: 4.069444445 + -4.069444445 = 0.000000000 0.000000000 + x = -4.123690402 + -4.069444445 x = -4.123690402 + -4.069444445 Combine like terms: -4.123690402 + -4.069444445 = -8.193134847 x = -8.193134847 Simplifying x = -8.193134847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.054245957, -8.193134847}Solution
x = {0.054245957, -8.193134847}
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