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Simplifying 6x2 + 30x + -82 = 0 Reorder the terms: -82 + 30x + 6x2 = 0 Solving -82 + 30x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + 15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + 15x + 3x2)' equal to zero and attempt to solve: Simplifying -41 + 15x + 3x2 = 0 Solving -41 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '13.66666667' to each side of the equation. -13.66666667 + 5x + 13.66666667 + x2 = 0 + 13.66666667 Reorder the terms: -13.66666667 + 13.66666667 + 5x + x2 = 0 + 13.66666667 Combine like terms: -13.66666667 + 13.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + 13.66666667 5x + x2 = 0 + 13.66666667 Combine like terms: 0 + 13.66666667 = 13.66666667 5x + x2 = 13.66666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 13.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 13.66666667 + 6.25 Combine like terms: 13.66666667 + 6.25 = 19.91666667 6.25 + 5x + x2 = 19.91666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 19.91666667 Calculate the square root of the right side: 4.46280928 Break this problem into two subproblems by setting (x + 2.5) equal to 4.46280928 and -4.46280928.Subproblem 1
x + 2.5 = 4.46280928 Simplifying x + 2.5 = 4.46280928 Reorder the terms: 2.5 + x = 4.46280928 Solving 2.5 + x = 4.46280928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.46280928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.46280928 + -2.5 x = 4.46280928 + -2.5 Combine like terms: 4.46280928 + -2.5 = 1.96280928 x = 1.96280928 Simplifying x = 1.96280928Subproblem 2
x + 2.5 = -4.46280928 Simplifying x + 2.5 = -4.46280928 Reorder the terms: 2.5 + x = -4.46280928 Solving 2.5 + x = -4.46280928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.46280928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.46280928 + -2.5 x = -4.46280928 + -2.5 Combine like terms: -4.46280928 + -2.5 = -6.96280928 x = -6.96280928 Simplifying x = -6.96280928Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.96280928, -6.96280928}Solution
x = {1.96280928, -6.96280928}
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