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Simplifying 0 = (-6x2) + -30x + 124 Reorder the terms: 0 = 124 + -30x + (-6x2) Solving 0 = 124 + -30x + (-6x2) Solving for variable 'x'. Combine like terms: 0 + -124 = -124 -124 + 30x + (6x2) = 124 + -30x + (-6x2) + -124 + 30x + (6x2) Reorder the terms: -124 + 30x + (6x2) = 124 + -124 + -30x + 30x + (-6x2) + (6x2) Combine like terms: 124 + -124 = 0 -124 + 30x + (6x2) = 0 + -30x + 30x + (-6x2) + (6x2) -124 + 30x + (6x2) = -30x + 30x + (-6x2) + (6x2) Combine like terms: -30x + 30x = 0 -124 + 30x + (6x2) = 0 + (-6x2) + (6x2) -124 + 30x + (6x2) = (-6x2) + (6x2) Combine like terms: (-6x2) + (6x2) = 0 -124 + 30x + (6x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-62 + 15x + (3x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-62 + 15x + (3x2))' equal to zero and attempt to solve: Simplifying -62 + 15x + (3x2) = 0 Solving -62 + 15x + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20.66666667 + 5x + x2 = 0 Move the constant term to the right: Add '20.66666667' to each side of the equation. -20.66666667 + 5x + 20.66666667 + x2 = 0 + 20.66666667 Reorder the terms: -20.66666667 + 20.66666667 + 5x + x2 = 0 + 20.66666667 Combine like terms: -20.66666667 + 20.66666667 = 0.00000000 0.00000000 + 5x + x2 = 0 + 20.66666667 5x + x2 = 0 + 20.66666667 Combine like terms: 0 + 20.66666667 = 20.66666667 5x + x2 = 20.66666667 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 = 20.66666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 20.66666667 + 6.25 Combine like terms: 20.66666667 + 6.25 = 26.91666667 6.25 + 5x + x2 = 26.91666667 Factor a perfect square on the left side: ((x) + 2.5)((x) + 2.5) = 26.91666667 Calculate the square root of the right side: 5.188127472 Break this problem into two subproblems by setting ((x) + 2.5) equal to 5.188127472 and -5.188127472.Subproblem 1
(x) + 2.5 = 5.188127472 Simplifying (x) + 2.5 = 5.188127472 x + 2.5 = 5.188127472 Reorder the terms: 2.5 + x = 5.188127472 Solving 2.5 + x = 5.188127472 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 = 5.188127472 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.188127472 + -2.5 x = 5.188127472 + -2.5 Combine like terms: 5.188127472 + -2.5 = 2.688127472 x = 2.688127472 Simplifying x = 2.688127472Subproblem 2
(x) + 2.5 = -5.188127472 Simplifying (x) + 2.5 = -5.188127472 x + 2.5 = -5.188127472 Reorder the terms: 2.5 + x = -5.188127472 Solving 2.5 + x = -5.188127472 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 = -5.188127472 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.188127472 + -2.5 x = -5.188127472 + -2.5 Combine like terms: -5.188127472 + -2.5 = -7.688127472 x = -7.688127472 Simplifying x = -7.688127472Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.688127472, -7.688127472}Solution
x = {2.688127472, -7.688127472}
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