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Simplifying 6x2 + -18x + -208 = 0 Reorder the terms: -208 + -18x + 6x2 = 0 Solving -208 + -18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-104 + -9x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-104 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying -104 + -9x + 3x2 = 0 Solving -104 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -34.66666667 + -3x + x2 = 0 Move the constant term to the right: Add '34.66666667' to each side of the equation. -34.66666667 + -3x + 34.66666667 + x2 = 0 + 34.66666667 Reorder the terms: -34.66666667 + 34.66666667 + -3x + x2 = 0 + 34.66666667 Combine like terms: -34.66666667 + 34.66666667 = 0.00000000 0.00000000 + -3x + x2 = 0 + 34.66666667 -3x + x2 = 0 + 34.66666667 Combine like terms: 0 + 34.66666667 = 34.66666667 -3x + x2 = 34.66666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 34.66666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 34.66666667 + 2.25 Combine like terms: 34.66666667 + 2.25 = 36.91666667 2.25 + -3x + x2 = 36.91666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 36.91666667 Calculate the square root of the right side: 6.075908711 Break this problem into two subproblems by setting (x + -1.5) equal to 6.075908711 and -6.075908711.Subproblem 1
x + -1.5 = 6.075908711 Simplifying x + -1.5 = 6.075908711 Reorder the terms: -1.5 + x = 6.075908711 Solving -1.5 + x = 6.075908711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.075908711 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.075908711 + 1.5 x = 6.075908711 + 1.5 Combine like terms: 6.075908711 + 1.5 = 7.575908711 x = 7.575908711 Simplifying x = 7.575908711Subproblem 2
x + -1.5 = -6.075908711 Simplifying x + -1.5 = -6.075908711 Reorder the terms: -1.5 + x = -6.075908711 Solving -1.5 + x = -6.075908711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.075908711 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.075908711 + 1.5 x = -6.075908711 + 1.5 Combine like terms: -6.075908711 + 1.5 = -4.575908711 x = -4.575908711 Simplifying x = -4.575908711Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.575908711, -4.575908711}Solution
x = {7.575908711, -4.575908711}
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