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Simplifying 6x2 + 150x + -80 = 0 Reorder the terms: -80 + 150x + 6x2 = 0 Solving -80 + 150x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + 75x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + 75x + 3x2)' equal to zero and attempt to solve: Simplifying -40 + 75x + 3x2 = 0 Solving -40 + 75x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + 25x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + 25x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + 25x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + 25x + x2 = 0 + 13.33333333 25x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 25x + x2 = 13.33333333 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 13.33333333 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 13.33333333 + 156.25 Combine like terms: 13.33333333 + 156.25 = 169.58333333 156.25 + 25x + x2 = 169.58333333 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 169.58333333 Calculate the square root of the right side: 13.02241657 Break this problem into two subproblems by setting (x + 12.5) equal to 13.02241657 and -13.02241657.Subproblem 1
x + 12.5 = 13.02241657 Simplifying x + 12.5 = 13.02241657 Reorder the terms: 12.5 + x = 13.02241657 Solving 12.5 + x = 13.02241657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 13.02241657 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.02241657 + -12.5 x = 13.02241657 + -12.5 Combine like terms: 13.02241657 + -12.5 = 0.52241657 x = 0.52241657 Simplifying x = 0.52241657Subproblem 2
x + 12.5 = -13.02241657 Simplifying x + 12.5 = -13.02241657 Reorder the terms: 12.5 + x = -13.02241657 Solving 12.5 + x = -13.02241657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -13.02241657 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.02241657 + -12.5 x = -13.02241657 + -12.5 Combine like terms: -13.02241657 + -12.5 = -25.52241657 x = -25.52241657 Simplifying x = -25.52241657Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.52241657, -25.52241657}Solution
x = {0.52241657, -25.52241657}
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