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Simplifying 6x2 = 30x + 10 Reorder the terms: 6x2 = 10 + 30x Solving 6x2 = 10 + 30x Solving for variable 'x'. Reorder the terms: -10 + -30x + 6x2 = 10 + 30x + -10 + -30x Reorder the terms: -10 + -30x + 6x2 = 10 + -10 + 30x + -30x Combine like terms: 10 + -10 = 0 -10 + -30x + 6x2 = 0 + 30x + -30x -10 + -30x + 6x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -10 + -30x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying -5 + -15x + 3x2 = 0 Solving -5 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -5x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -5x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 1.666666667 -5x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -5x + x2 = 1.666666667 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 = 1.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.666666667 + 6.25 Combine like terms: 1.666666667 + 6.25 = 7.916666667 6.25 + -5x + x2 = 7.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.916666667 Calculate the square root of the right side: 2.813657169 Break this problem into two subproblems by setting (x + -2.5) equal to 2.813657169 and -2.813657169.Subproblem 1
x + -2.5 = 2.813657169 Simplifying x + -2.5 = 2.813657169 Reorder the terms: -2.5 + x = 2.813657169 Solving -2.5 + x = 2.813657169 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 = 2.813657169 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.813657169 + 2.5 x = 2.813657169 + 2.5 Combine like terms: 2.813657169 + 2.5 = 5.313657169 x = 5.313657169 Simplifying x = 5.313657169Subproblem 2
x + -2.5 = -2.813657169 Simplifying x + -2.5 = -2.813657169 Reorder the terms: -2.5 + x = -2.813657169 Solving -2.5 + x = -2.813657169 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 = -2.813657169 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.813657169 + 2.5 x = -2.813657169 + 2.5 Combine like terms: -2.813657169 + 2.5 = -0.313657169 x = -0.313657169 Simplifying x = -0.313657169Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.313657169, -0.313657169}Solution
x = {5.313657169, -0.313657169}
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