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Simplifying 6x2 = 2x + 30 Reorder the terms: 6x2 = 30 + 2x Solving 6x2 = 30 + 2x Solving for variable 'x'. Reorder the terms: -30 + -2x + 6x2 = 30 + 2x + -30 + -2x Reorder the terms: -30 + -2x + 6x2 = 30 + -30 + 2x + -2x Combine like terms: 30 + -30 = 0 -30 + -2x + 6x2 = 0 + 2x + -2x -30 + -2x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -30 + -2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -15 + -1x + 3x2 = 0 Solving -15 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.3333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.3333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.3333333333x + x2 = 0 + 5 -0.3333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.3333333333x + x2 = 5 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 5 + 0.02777777779 Combine like terms: 5 + 0.02777777779 = 5.02777777779 0.02777777779 + -0.3333333333x + x2 = 5.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 5.02777777779 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 2.242270675 and -2.242270675.Subproblem 1
x + -0.1666666667 = 2.242270675 Simplifying x + -0.1666666667 = 2.242270675 Reorder the terms: -0.1666666667 + x = 2.242270675 Solving -0.1666666667 + x = 2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 2.242270675 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.242270675 + 0.1666666667 x = 2.242270675 + 0.1666666667 Combine like terms: 2.242270675 + 0.1666666667 = 2.4089373417 x = 2.4089373417 Simplifying x = 2.4089373417Subproblem 2
x + -0.1666666667 = -2.242270675 Simplifying x + -0.1666666667 = -2.242270675 Reorder the terms: -0.1666666667 + x = -2.242270675 Solving -0.1666666667 + x = -2.242270675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -2.242270675 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.242270675 + 0.1666666667 x = -2.242270675 + 0.1666666667 Combine like terms: -2.242270675 + 0.1666666667 = -2.0756040083 x = -2.0756040083 Simplifying x = -2.0756040083Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4089373417, -2.0756040083}Solution
x = {2.4089373417, -2.0756040083}
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