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Simplifying 45x2 + -492x + -2466 = 0 Reorder the terms: -2466 + -492x + 45x2 = 0 Solving -2466 + -492x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-822 + -164x + 15x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-822 + -164x + 15x2)' equal to zero and attempt to solve: Simplifying -822 + -164x + 15x2 = 0 Solving -822 + -164x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -54.8 + -10.93333333x + x2 = 0 Move the constant term to the right: Add '54.8' to each side of the equation. -54.8 + -10.93333333x + 54.8 + x2 = 0 + 54.8 Reorder the terms: -54.8 + 54.8 + -10.93333333x + x2 = 0 + 54.8 Combine like terms: -54.8 + 54.8 = 0.0 0.0 + -10.93333333x + x2 = 0 + 54.8 -10.93333333x + x2 = 0 + 54.8 Combine like terms: 0 + 54.8 = 54.8 -10.93333333x + x2 = 54.8 The x term is -10.93333333x. Take half its coefficient (-5.466666665). Square it (29.88444443) and add it to both sides. Add '29.88444443' to each side of the equation. -10.93333333x + 29.88444443 + x2 = 54.8 + 29.88444443 Reorder the terms: 29.88444443 + -10.93333333x + x2 = 54.8 + 29.88444443 Combine like terms: 54.8 + 29.88444443 = 84.68444443 29.88444443 + -10.93333333x + x2 = 84.68444443 Factor a perfect square on the left side: (x + -5.466666665)(x + -5.466666665) = 84.68444443 Calculate the square root of the right side: 9.202415141 Break this problem into two subproblems by setting (x + -5.466666665) equal to 9.202415141 and -9.202415141.Subproblem 1
x + -5.466666665 = 9.202415141 Simplifying x + -5.466666665 = 9.202415141 Reorder the terms: -5.466666665 + x = 9.202415141 Solving -5.466666665 + x = 9.202415141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.466666665' to each side of the equation. -5.466666665 + 5.466666665 + x = 9.202415141 + 5.466666665 Combine like terms: -5.466666665 + 5.466666665 = 0.000000000 0.000000000 + x = 9.202415141 + 5.466666665 x = 9.202415141 + 5.466666665 Combine like terms: 9.202415141 + 5.466666665 = 14.669081806 x = 14.669081806 Simplifying x = 14.669081806Subproblem 2
x + -5.466666665 = -9.202415141 Simplifying x + -5.466666665 = -9.202415141 Reorder the terms: -5.466666665 + x = -9.202415141 Solving -5.466666665 + x = -9.202415141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.466666665' to each side of the equation. -5.466666665 + 5.466666665 + x = -9.202415141 + 5.466666665 Combine like terms: -5.466666665 + 5.466666665 = 0.000000000 0.000000000 + x = -9.202415141 + 5.466666665 x = -9.202415141 + 5.466666665 Combine like terms: -9.202415141 + 5.466666665 = -3.735748476 x = -3.735748476 Simplifying x = -3.735748476Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.669081806, -3.735748476}Solution
x = {14.669081806, -3.735748476}
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